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RADAR SYSTEM ENGINEERING

MASSACHUSETTS INSTITUTE OF TECHNOLOGY

RADIATION LABORATORY SERIES

Board of Editors

Louis N. Ridenour, Editor-in-Chief
George B. Collins, Deputy Editor-in-Chief

Britton Chance, S. A. Goudsmit, R. G. Herb, Hubert M. James, Julian K. Knipp,
James L. Lawson, Leon B. Linford, Carol G. Montgomery, C. Newton, Albert
M. Stone, Louis A. Turner, George E. Valley, Jr., Herbert H. Wheaton

1. Radar System Engineering— Ridenour

2. Radar Aids to Navigation— Hall

3. Radar Beacons— Roberts

4. Loran— Pierce, McKenzie, and Woodward

5. Pulse Generators— Glasoe and Lebacqz

6. Microwave Magnetrons— Collins

7. Klystrons and Microwave Triodes— Hamilton, Knipp, and Kuper

8. Principles of Microwave Circuits— Montgomery, Dicke, and Purcell

9. Microwave Transmission Circuits— Ragan

10. Waveguide Handbook— Marcuvilz

11. Technique of Microwave Measurements— Montgomery

12. Microwave Antenna Theory and Design —Silver

13. Propagation of Short Radio Waves— Kerr

14. Microwave Duplexers— Smullin and Montgomery

15. Crystal Rectifiers— Torrey and Whitmer

16. Microwave Mixers— Pound

17. Components Handbook— Blackburn

18. Vacuum Tube Amplifiers— Valley and Wallman

19. Waveforms— Chance, Hughes, MacNichol, Sayre, and Williams

20. Electronic Time Measurements— Chance, Hulsizer, MacNichol,

and Williams

21. Electronic Instruments— Greenwood, Holdam, and MacRae

22. Cathode Ray Tube Displays— Soller, Starr, and Valley

23. Microwave Receivers— Van Voorhis

24. Threshold Signals— Lawson and Uhlenbeck

25. Theory of Servomechanisms— James, Nichols, and Phillips

26. Radar Scanners and Radomes— Cady, Karelitz, and Turner

27. Computing Mechanisms and Linkages— Svoboda

28. Index— Henney

RADAR SYSTEM

ENGINEERING

ici

2EKCE LIBR

Edited by

LOUIS N. RIDENOUR

PROFESSOR OF PHYSICS
UNIVERSITY OF PENNSYLVANIA

First Fruition

NEW YORK AND LONDON
McGRAW-HILL BOOK COMPANY, INC.
1947

(

RADAR SYSTEM ENGINEERING

PRINTED IN THE UNITED STATES OF AMERICA

All rights reserved. This hook, or
parts thereof, may not be reproduced
in any form without permission of
the publishers.

THE MAPLE PRESS COMPANY, YORK

PA.

RADAR SYSTEM ENGINEERING

EDI TORI AL STAFF
Louis N. Ridenour
Avis M. Clarke

CONTRIBUTING AUTHORS

L. Y. Beers
B. V. Bowden
W. M. Cady
R. E. Clapp
G. B. Collins
A. G. Emslie
W. W. Hansen

L. J. Haworth
R. G. Herb

M. M. Hubbard
P. C. Jacobs

M. H. Johnson
W. H. Jordan
J. V. Lebacqz
F. B. Lincoln
R. A. McConnell

F. J. Mehringer
R. D. O’Neal

C. F. J. Overhage
E. C. Pollard
E. M. Purcell
L. N. Ridenour

C. V. Robinson
A. J. F. SlEGERT
R. L. Sinsheimer

D. C. Soper

G. F. Tape

L. A. Turner

M. G. White
A. E. Whitford
J. M. Wolf

C. L. Zimmerman

Foreword

T he tremendous research and development effort that went into the
development of radar and related techniques during World War II
resulted not only in hundreds of radar sets for military (and some for
possible peacetime) use but also in a great body of information and new
techniques in the electronics and high-frequency fields. Because this
basic material may be of great value to science and engineering, it seemed
most important to publish it as soon as security permitted.

The Radiation Laboratory of MIT, which operated under the super¬
vision of the National Defense Research Committee, undertook - the great
task of preparing these volumes. The work described herein, however, is
the collective result of work done at many laboratories, Army, Navy,
university, and industrial, both in this country and in England, Canada,
and other Dominions.

The Radiation Laboratory, once its proposals were approved and
finances provided by the Office of Scientific Research and Development,
chose Louis N. Ridenour as Editor-in-Chief to lead and direct the entire
project. An editorial staff was then selected of those best qualified for
this type of task. Finally the authors for the various volumes or chapters
or sections were chosen from among those experts who were intimately
familiar with the various fields, and who were able and willing to write
the summaries of them. This entire staff agreed to remain at work at
MIT for six months or more after the work qf the Radiation Laboratory
was complete. These volumes stand as a monument to this group.

These volumes serve as a memorial to the unnamed hundreds and
thousands of other scientists, engineers, and others who actually carried
on the research, development, and engineering work the results of which
are herein described. There were so many involved in this work and they
worked so closely together even though often in widely separated labora¬
tories that it is impossible to name or even to know those who contributed
to a particular idea or development. Only certain ones who wrote reports
or articles have even been mentioned. But to all those who contributed
in any way to this great cooperative development enterprise, both in this
country and in England, these volumes are dedicated.

L. A. DuBridge.

Preface

T he earliest plans for the Radiation Laboratory Series, made in the fall
of 1944, envisaged only books concerned with the basic microwave
and electronic theory and techniques that had been so thoroughly devel¬
oped during the wartime work on radar. These plans were laid aside for
a time when it became clear in this country that several months of fighting
remained in the European war.

When work on the Series was resumed in the early summer of 1945, the
books planned, as before, dealt with basic matters and with techniques.
Every effort was made to point out the general applicability of the work
reported and to avoid special emphasis on its application to radar, since
radar itself was thought to have only a limited importance.

The end of the Pacific war made it possible to put more effort on the
job of preparing the Series than had been available earlier. The books
on theory and techniques having been planned as comprehensively as
appeared to be worth while, the work was extended by the addition of
five books concerned with radar and allied systems.

Of those five books, this is the only one that deals with radar itself.
One book takes up the use of radar in navigation, one concerns the design
of radar scanners and radomes, one treats the design and construction of
beacons, and one describes hyperbolic navigational systems—in particular
Loran.

This book is intended to serve as a general treatise and reference book
on the design of radar systems. No apology seems to be needed for the
fact that it deals primarily—though by no means altogether—with micro-
wave pulse radar. Thousands of times as much work has gone into pulse
radar as into any other kind, and the overwhelming majority of this work
has been concerned with microwave pulse radar. The superiority of
microwaves for almost all radar purposes is now clear.

The first eight chapters of this book are intended to provide an intro¬
duction to the field of radar and a general approach to the problems of
system design. Chapters 9 through 14 take up the leading design con¬
siderations for the various important components that make up a radar
set. These chapters are so thorough in their treatment that Chap. 15,
which gives two fairly detailed examples of actual system design, can be
quite brief. Chapters 16 and 17 take up two new and important ancillary

PREFACE

techniques that are not dealt with fully elsewhere in the Series: moving-
target indication and the transmission of radar displays to a remote
indicator by radio means.

For fuller information than can be found in this book on any detailed
point of design, the reader is referred to one of the other books of the
Series. In a sense, this book specializes to radar the techniques reported
more fully elsewhere in the Series.

Radar is a very simple subject, and no special mathematical, physical,
or engineering background is needed to read and understand this book.

Because the book covers the entire field of effort of the Radiation
Laboratory and the other wartime radar establishments, its contributing
authors are more numerous than those listed for most other volumes of
this series. I am especially grateful to L. J. Haworth and to E. M.
Purcell, whose contributions have been more extensive than those of
other authors, and whose advice on editorial problems has often been
extremely helpful. In addition to the authors already listed, whose
names appear in the book in connection with the material they have
written, I wish to thank the following men for their work in provid¬
ing essential background material that did not eventually find its way
into the book: R. M. Alexander, A. H. Brown, J. F. Carlson, M. A.
Chaffee, L. M. Hollingsworth, E. L. Hudspeth, R. C. Spencer, and I. G.
Swope. Changing plans for the book also reduced the acknowledged
contribution of E. C. Pollard far below the very considerable quantity of
material he prepared.

I owe an apology to all the authors for the liberty I have often
taken in altering their original text to fit the final framework of the
book and my own ideas of style. Because most authors left the Labora¬
tory immediately on finishing their writing, and much of the editorial
work had to be deferred until the book was substantially complete, it has
not always been possible to adjust with the authors the alterations in their
manuscripts that have seemed desirable to me.

The general acknowledgments I owe as Editor-in-Chief of the Series
are set forth in the Series Index. In connection with the preparation
of this book, however, it is a pleasure to thank Dr. B. V. Bowden, of the
British Air Commission, not only for his assistance as an author but also
for his general comments on the book as a whole. I am grateful to
Lois Capen for her work in following the preparation of illustrations, and
to Phyllis Brown for general secretarial assistance.

Cambridge, Mass.
June , 1946

Louis N. Ridenour.

Contents

FOREWORD by L. A. DuBridge .vii

PREFACE. ix

Chap. 1. INTRODUCTION. I

1 ■ 1 What Radar Does. 1

1-2 How Radar Works. 3

1 -3 Components of a Radar System. 6

1-4 The Performance of Radar. 8

1-5 Radar Systems. 12

1-6 The Early History of Radar. . 13

1- 7 Wartime Radar Development in the U.S. 15

Chap. 2. THE RADAR EQUATION. 18

The Radar Equation for Free-space Propagation 18

21 The Meaning of Free-space Propagation.18

2- 2 Antenna Gain and Receiving Cross Section. . . . . 19

2-3 Scattering Cross Section of the Target ... ..... 21

2-4 The Radar Equation. 21

2-5 Beams of Special Shapes. 22

2-6 The Beacon Equation.27

The Minimum Detectable Signal.28

2-7 Noise.28

2-8 Receivers, Ideal and Real.30

2-9 Receiver Bandwidth and Pulse Energy.33

2-10 The Statistical Problem. 35

2T1 Effect of Storage on Radar Performance . .. 41

Microwave Propagation.47

2-12 Propagation over a Reflecting Surface 47

2-13 The Round Earth. 53

2-14 Superrefraction.55

2- 15 Attenuation of Microwaves in the Atmosphere ..58

Chap. 3. PROPERTIES OF RADAR TARGETS.63

Simple Targets.63

3- 1 Cross Section Expressed in Terms of the Field Quantities ... 63

3-2 Rayleigh Scattering from a Small Sphere. 63

3-3 Scattering of a Plane Wave by a Sphere . 64

3-4 Approximations for Large Metal Targets . . 65

3-5 The Corner Reflector. 67

3-6 Target Shaping to Diminish Cross Section. 68

3-7 Use of Absorbent Materials. 69

CONTENTS

xii

Complicated Targets. 73

3-8 Return from Two Isotropic Targets. 73

3-9 Actual Complex Targets.75

310 Compound Targets Extended through Space.81

311 Extended Surface Targets.85

Ground Painting by Airborne Radar. .88

3-12 Specular and Diffuse Reflection.89

3-13 Sea Return and Ground Return.92

3T4 Mountain Relief.96

3-15 Structures.99

3- 16 Cities.101

3T7 Navigation.108

Chap. 4. LIMITATIONS OF PULSE RADAR.116

41 Range, Pulse-repetition Frequency, and Speed of Scan .116

4- 2 Bandwidth, Power, and Information-rate. 121

4-3 Pulse Radar and C-w Radar.123

4- 4 Clutter.124

Chap. 5. C-W RADAR SYSTEMS.127

5T General Considerations.. . . . ..127

5- 2 Transmitted Spectra. 129

5-3 Effect of Target.130

5-4 Class of Systems Considered.131

5-5 Utility of C-w Systems. . ..132

Specific Systems. 132

5-6 Simple Doppler System. 132

5-7 Range-measuring Doppler System.139

5-8 F-m Range-measuring System. . .. 143

5 9 Multiple Target F-m Range Measurement . .147

5- 10 Alternative F-m Ranging System.149

511 Pulse-modulated Doppler System. 150

512 Summary.157

Chap. 6. THE GATHERING AND PRESENTATION OF RADAR DATA 160
61 Influence of Operational Requirements.160

Types of Radar Indicators.161

6- 2 Definitions.161

6-3 Summary of Indicator Types.163

6-4 One-dimensional Deflection-modulated Displays.164

6-5 Representation of the Horizontal Plane. 167

6-6 Plane Displays Involving Elevation 171

6-7 Three-dimensional Displays.174

6-8 Error Indicators.175

CONTENTS

xiii

Examples of the Major Operational Requirements.175

6-9 Early Aircraft Warning Radar.175

6-10 PPI Radar for Search, Control, and Pilotage.182

611 Height-finding Involving Ground Reflection.184

6-12 Height-finding with a Free-space Beam.187

613 Homing.196

6- 14 Precision Tracking of a Single Target.203

6T5 Precision Tracking during Rapid Scan.210

Chap. 7. THE EMPLOYMENT OF RADAR DATA.213

71 The Signal and Its Use.213

External Aids to Radar Use.214

7- 2 Aids to Individual Navigation.214

7-3 Aids to Plotting and Control.218

7-4 The Relay of Radar Displays.225

Examples of Radar Organizations.. ... 226

7-5 Radar in the RAF Fighter Command. 226

7-6 The U.S. Tactical Air Commands.229

7-7 Close Control with SCR-584 . 238

7- 8 Teleran.240

Chap. 8. RADAR BEACONS.243

Radar-beacon Systems.246

8- 1 Types of Radar-beacon Systems.246

8 2 Systems Planning.250

8-3 General Identification System—IFF.251

8-4 Radar Interrogation vs. Special Interrogators.252

8-5 Independence of Interrogation and Reply... 254

8-6 Frequency Considerations. 260

Coding.263

8-7 Interrogation Codes.263

8-8 Reply Codes.264

Statistical Considerations. 265

8- 9 Traffic Capacity.265

8T0 Unsynchronized Replies.268

Chap. 9. ANTENNAS, SCANNERS, AND STABILIZATION.271

9- 1 The .Antenna Equation.271

9-2 Round and Cut Paraboloid Antennas.272

9-3 Fan Beams.274

9-4 Nonscanning Antennas.277

9-5 Construction of Radar Antennas.279

Radar Scanning Patterns.280

9-6 Simple Scans.281

9-7 Complex Scans.281

XIV

CONTENTS

Mechanical Scanners.282

9-8 The Kinematics of Mechanical Scanners.282

9-9 The Weight of Mechanical Scanners.283

910 R-f Transmission Lines.283

9T1 Data Transmission. 284

9-12 Examples of Mechanical Scanners.284

Electrical Scanners.291

9-13 TheAN/APQ-7 (Eagle) Scanner. 291

9 14 SchwarzBchild Antenna.295

9- 15 SCI Height Finder.298

9T6 Other Types of Electrical Scanners.302

The Stabilization Problem.304

9T7 Stabilization of the Beam. 305

918 Data Stabilization.311

919 Installation of Airborne Scanners.312

9-20 Installation of Surface-based Scanners.313

9-21 Radomes.314

9-22 Streamlining.315

9-23 Electrical Transmission. 316

9-24 Structural Design of Radomes.316

9- 25 Examples of Radomes. 317

Chap. 10. THE MAGNETRON AND THE PULSER.320

The Magnetron.320

101 Construction.321

10-2 The Resonant System.325

10-3 Electron Orbits and the Space Charge . . 330

10- 4 Performance Charts and Rieke Diagrams ..336

10-5 Magnetron Characteristics Affecting Over-all Systems Design 340

10-6 Magnetron Characteristics Affecting Pulser Design.352

The Pulser.355

10-7 Pulser Circuits.356

10-8 Load Requirements.362

10 9 The Hard-tube Pulser. 367

10- 10 Line-type Pulsers.373

10- 11 Miscellaneous Components.383

Chap. 11. R-F COMPONENTS.391

11- 1 The R-f Transmission Problem. 391

11-2 Coaxial Lines.393

11-3 Waveguide.398

11-4 Resonant Cavities. 405

11-5 Duplexing and TR Tubes.407

CONTENTS

Microwave Components of The Receiver.411

11-6 The Mixer Crystal.412

11-7 The Local Oscillator.414

11-8 The Mixer.416

11-9 Automatic Frequency Control.418

Mounting the R-f Parts.419

11-10 Reasons for an R-f Package.419

11-11 Design Considerations for the R-f Head.421

11- 12 Illustrative Examples of R-f Heads.425

Chap. 12. THE RECEIVING SYSTEM—RADAR RECEIVERS ... 433

Introduction . ..433

12- 1 The Role of the Receiving System.433

12-2 A Typical Receiving System.435

The Receiver.441

12-3 Special Problems in Radar Receivers.441

12-4 I-f Amplifier Design.442

12-5 Second Detector.449

12-6 Video Amplifiers.450

12-7 Automatic Frequency Control.453

12-8 Protection against Extraneous Radiation.457

Typical Receivers.460

12-9 A General-purpose Receiver.462

1210 Lightweight Airborne Receiver.464

12- 11 An Extremely Wide-band Receiver.470

Chap. 13. THE RECEIVING SYSTEM—INDICATORS.475

The Cathode-ray Tube.475

13- 1 Electrical Properties of Cathode-ray Tubes.475

13-2 Cathode-ray Tube Screens.479

13-3 The Selection of the Cathode-ray Tube.483

Coordination with the Scanner.486

13-4 Angle-data Transmitters.486

13-5 Electromechanical Repeaters.490

Basic Electrical Circuits.492

13-6 Amplifiers.492

13-7 The Generation of Rectangular Waveforms. 496

13-8 The Generation of Sharp Pulses. 501

13-9 Electronic Switches.503

13-10 Sawtooth Generators.510

Indices.513

13-11 Angle Indices.514

13-12 Range and Height Indices; Synchronization 518

XVI

CONTENTS

Display Synthesis .524

13-13 The Design of A-scopes.524

1314 B-Scope Design.528

13-15 Plan-position Indicator.532

13-16 The “Resolved Time Base” Method of PPI Synthesis .... 534

13-17 Resolved-current PPI.538

13-18 The Method of Pre-time-base Resolution.544

13-19 The Range-height Indicator.545

Signal Discrimination, Resolution, and Contrast .548

13-20 Resolution and Contrast.548

13- 21 Special Receiving Techniques for Air-to-land Observation .... 550

Chap. 14. PRIME POWER SUPPLIES FOR RADAR.555

Aircraft Systems .555

14 1 Choice of Frequency.555

14- 2 Wave Shape.557

14-3 Direct-driven Generators. . 557

14-4 Motor-alternator Sets.561

14-5 Voltage Regulators.563

14-6 Speed Regulators.571

14-7 Dvnamotors.579

14-8 Vibrator Power Supplies.581

14-9 Summary of Recommendations for Aircraft Radar Power . . . 582

Ground and Shipboard Systems .583

14-10 Fixed Locations. 583

14-11 Large Systems Where No Commercial Power Is Available. . 584

14-12 Smaller Mobile Units.585

14-13 Ultraportable Units.585

14- 14 Ship Radar Systems.586

Chap. 15. EXAMPLES OF RADAR SYSTEM DESIGN.588

15- 1 Introduction. . 588

15-2 The Need for System Testing.590

Design of a High-performance Radar for Air Surveillance and
Control .592

15-3 Initial Planning and Objectives.592

15-4 The Range Equation.595

15-5 Choice of Pulse Length.596

15-6 Pulse Recurrence Frequency.598

15-7 Azimuth Scan Rate.599

15-8 Choice of Beam Shape.600

15-9 Choice of Wavelength.604

15-10 Components Design.606

15-11 Modifications and Additions.609

CONTENTS xvii

Design of a Lightweight Airborne Radar for Navigation.611

15-12 Design Objectives and Limitations.611

15-13 General Design of the AN/APS-10.614

15- 14 Detailed Design of the AN/APS-10.616

Chap. 16. MOVING-TARGET INDICATION . 626

Introduction. 626

16- 1 The Role of Moving-Target Indication.626

16 2 Basic Principles of MTI.626

16-3 A Practical MTI System.632

16-4 Alternative Methods for Obtaining Coherence.635

Performance Criteria and Choice of System Constants.638

16-5 Stability Requirements.638

16-6 Internal Clutter Fluctuations.642

16-7 Fluctuations Due to Scanning.644

16-8 Receiver Characteristics . :.646

16-9 Target Visibility.649

16-10 Choice of System Constants.653

Moving-Target Indication on a Moving System.655

16-11 Compensation for Velocity of System.655

1612 The Noncoherent Method.656

16-13 Beating Due to Finite Pulse Packet.657

Component Design.658

16-14 The Transmitter and Its Modulator.658

16-15 The Stable Local Oscillator.659

16-16 The Coherent Oscillator.662

16-17 The Receiver.665

16-18 The Supersonic Delay Line.667

16-19 Delay-line Signal Circuits . . ..672

16-20 Delay-line Trigger Circuits.675

16- 21 Special Test Equipment.677

Chap. 17. RADAR RELAY.680

Introduction. 680

17 1 The Uses of Radar Relay.680

17- 2 The Elements of Radar Relay.681

Methods of Scanner Data Transmission.682

17-3 General Methods of Scanner Data Transmission.683

17-4 Methods of Combating Interference.685

17-5 The Method of Incremental Angle.689

17-6 The Phase-shift Method.695

17-7 Methods of Relaying Sine and Cosine.701

17-8 Pulse Method for Relaying Sine and Cosine.705

17-9 Comparison of Synchronization Methods. .711

xviii CONTENTS

The Radio-frequency Equipment .713

1710 Antennas, Frequencies, and the Radiation Path.713

1711 General Transmitter and Receiver Considerations.717

1712 A 300-Mc/sec Amplitude-modulated Equipment.719

17-13 A 100-Mc/sec Frequency-modulated Equipment.721

1714 Microwave System for Point-to-point Service.723

Radar Relay Systems.726

17-15 A Ground-to-ground Relay System. 726

17-16 Relay System for Airborne Radar.732

INDEX.737

CHAPTER 1

INTRODUCTION

By Louis N. Ridenour

1-1. What Radar Does. —Radar is an addition to man’s sensory
equipment which affords genuinely new facilities. It enables a certain
class of objects to be “seen”—that is, detected and located—at distances
far beyond those at which they could be distinguished by the unaided
eye. This “seeing” is unimpaired by night, fog, cloud, smoke, and most
other obstacles to ordinary vision. Radar further permits the measure¬
ment of the range of the objects it “sees” (this verb will hereafter be used
without apologetic quotation marks) with a convenience and precision
entirely unknown in the past. It can also measure the instantaneous
speed of such an object toward or away from the observing station in a
simple and natural way.

The superiority of radar to ordinary vision lies, then, in the greater
distances at which seeing is possible with radar, in the ability of radar to
work regardless of light condition and of obscuration of the object being
seen, and in the unparalled ease with which target range and its rate of
change can be measured. In certain other respects radar is definitely
inferior to the eye. The detailed definition of the picture it offers is very
much poorer than that afforded by the eye. Even the most advanced
radar equipment can only show the gross outlines of a large object, such
as a ship; the eye can—if it can see the ship at all—pick out fine details
such as the rails on the deck and the number or character of the flags at
the masthead. Because of this grossness of radar vision, the objects
that can usefully be seen by radar are not as numerous as the objects
that can^be distinguished by the eye. Radar is at its best in dealing with
isolated targets located in a relatively featureless background, such as
aircraft in the air, ships on the open sea, islands and coastlines, cities in
a plain, and the like. Though modern high-definition radar does afford
a fairly detailed presentation of such a complex target as a city viewed
from the air (see, for example, Fig. 3-35), the radar picture of such a
target is incomparably poorer in detail than a vertical photograph taken
under favorable conditions would be.

One further property of radar is worth remarking: its freedom from
difficulties of perspective. By suitable design of the equipment, the
picture obtained from a radar set can be presented as a true plan view,

INTRODUCTION

[Sec. 11

regardless of the obliquity of the angle from which the target is seen.
This is shown clearly in Fig. IT, which compares with a chart of the tip
of Cape Cod a radar picture and a direct photograph taken simultaneously

(e)

Fig. 1-1.—Cape Cod: (a) radar photograph, ( b ) map, (c) optical photograph from air¬
craft carrying the radar set. The radar photograph shown in (a) is one of the earliest
pictures taken with 3-cm airborne equipment (summer 1942).

from an airplane flying over Cape Cod Bay. There can be little question
of the superiority of the radar picture for most purposes, especially in
view of the fact that had it been night, or had the weather been foggy,

Sec. 1-2]

HOW RADAR WORKS

the radar picture would have been unaffected while photography or
ordinary vision would have been useless.

1-2. How Radar Works. —The coined word radar is derived from the
descriptive phrase “radio detection and ranging.” Radar works by
sending out radio waves from a transmitter powerful enough so that
measurable amounts of radio energy will be reflected from the objects to
be seen by the radar to a radio receiver usually located, for convenience,
at the same site as the transmitter. The properties of the received echoes
are used to form a picture or to determine certain properties of the objects
that cause the echoes. The radar transmitter may send out c-w signals,
or frequency-modulated c-w signals, or signals modulated in other ways.
Many schemes based on transmissions of various sorts have been proposed
and some of them have been used. Chapter 5 of this book treats the
general radar problem, in which any scheme of transmitter modulation
may be used, in a very fundamental and elegant way.

Despite the great number of ways in which a radar system can in
principle be designed, one of these ways has been used to such an over¬
whelming degree that the whole of this book, with the exception of Chap.
5, is devoted to it. When radar is mentioned without qualification in
this book, pulse radar will be meant. No apology for this specialization
is needed. Thousands of times as much effort as that expended on all
other forms of radar put together has gone into the remarkably swift
development of pulse radar since its origin in the years just before World
War II.

In pulse radar, the transmitter is modulated in such a way that it
sends out very intense, very brief pulses of radio energy at intervals that
are spaced rather far apart in terms of the duration of each pulse. During
the waiting time of the transmitter between pulses, the receiver is active.
Echoes are received from the nearest objects soon after the transmission
of the pulse, from objects farther away at a slightly later time, and so on.
When sufficient time has elapsed to allow for the reception of echoes from
the most distant objects of interest, the transmitter is keyed again to
send another very short pulse, and the cycle repeats. Since the radio
waves used in radar are propagated with the speed of light, c, the delay
between the transmission of a pulse and the reception of the echo from
an object at range R will be

T =

2 R

- 1

( 1 )

the factor 2 entering because the distance to the target has to be traversed
twice, once out and once back. Figure 1-2 shows schematically the
principle of pulse radar.

The linear relation between delay time and range shown in Eq. (1) is

Radar

Fig. 1-2.—The principle of pulse radar, (a) Pulse has just been emitted from radar
set. ( b ) Pulse reaches target, (c) Scattered energy returns from target; transmitted pulse
carries on. (d) Echo pulse reaches radar.

Sec. 1-2]

HOW RADAR WORKS

the clue to the ease with which range can be measured by radar. Range
measurement is reduced to a measurement of time, and time can be
measured perhaps more accurately than any other basic physical quan¬
tity. Because the velocity of light is high, the intervals of time that
must be measured in radar are short. Numerically, the range corre¬
sponding to a given delay time is 164 yd for each microsecond elapsing
between the transmission of the pulse and the reception of the echo. If
it is desired to measure range to a precision of 5 yd, which is necessary in
some applications of radar, time intervals must be measured with a

Fig. 1*3.—The simplest radar display, the A-scope. The echo at the right is from, the moon.

precision better than t*V jusec. Modern electronic timing and display
techniques have been developed to such a point that this can readily be
done.

One of the simplest ways in which radar echo signals can be displayed
is shown in Fig. 1-3. The beam of a cathode-ray tube is caused to begin
a sweep from left to right across the face of the tube at the instant a pulse
is sent from the transmitter. The beam is swept to the right at a uniform
rate by means of a sawtooth 'waveform applied to the horizontal deflection
plates of the CRT. The output signals of the radar receiver are applied
to the vertical deflection plates. To ensure that the weakest signals
that are at all detectable are not missed, the over-all gain of the receiver
is high enough so that thermal noise originating in the receiver (Sec. 2-7)
is perceptible on the display. The two signals that rise significantly
above this noise in Fig. T3 are, on the left, the “tail” of the transmitted

INTRODUCTION

[Sec. 1-3

pulse leaking into the receiver, and on the right, the echo signal from a
radar target. The target in the particular case of Fig. 1-3 is the earth’s
moon.

The measurement of range by means of radar is thus a straightforward
problem of time measurement. It is also desirable to be able to measure
the direction in which a target lies as viewed from a radar station. In
principle, this can be done on the basis of triangulation, using range
information on the same target from two or more separate radar locations.
Although this method permits of great accuracy and has occasionally
been used for special purposes, it is far more desirable from the stand¬
point of simplicity and flexibility to measure direction, as well as range,
from a single radar station. Measurement of target bearing was made
possible by the development of radio techniques on wavelengths short
enough to permit the use of highly directional antennas, so that a more
or less sharp beam of radiation could be produced by an antenna of
reasonable physical size.

When the pulses are sent out in such a beam, echoes will be received
only from targets that lie in the direction the beam is pointing. If the
antenna, and hence the radar beam, is swept or scanned around the
horizon, the strongest echo will be received from each target when
the beam is pointing directly toward the target, weaker echoes when the
beam is pointed a little to one side or the other of the target, and no echo
at all when it is pointing in other directions. Thus, the bearing of a
target can be determined by noting the bearing of the radar antenna
when that target gives the strongest echo signal. This can be done in a
variety of ways, and more precise and convenient means for determining
target bearing by means of radar have been developed (Chap. 6), but the
method described here illustrates the basic principle.

It is convenient to arrange the radar display so that, instead of show¬
ing target range only, as in Fig. T3, it shows the range and angular
disposition of all targets at all azimuths. The plan-position indicator,
or PPI, is the most common and convenient display of this type. Figure
11 is a photograph of a PPI-scope. The direction of each echo signal
from the center of the PPI shows its direction from the radar; its distance
from the center is proportional to target range. Many other forms of
indication are convenient for special purposes; the various types of indi¬
cator are catalogued in Chap. 6.

1-3. Components of a Radar System. —A radar set can be considered
as separable, for the purposes of design and description, into several major
components concerned with different functions. Figure 1-4 is a block
diagram of a simple radar set broken up into the components ordinarily
distinguished from one another.

In the set illustrated in Fig. 1-4, a cycle of operation is begun by the

Sec. 13]

COMPONENTS OF A RADAR SYSTEM

firing of the modulator. This sends a high-power, high-voltage pulse to
the magnetron, which is the type of transmitting tube almost universally
used in modern radar. For the brief duration of the modulator pulse,
which may typically be 1 ,usec, the magnetron oscillates at the radio
frequency for which it is designed, usually some thousands of megacycles
per second. The r-f pulse thus produced travels down the r-f transmis¬
sion line shown by double lines in Fig. 1-4, and passes through the two
switches designated as TR and ATR. These are gas-discharge devices
of a very special sort. The gas discharge is started by the high-power

r-f pulse from the transmitter, and maintained for the duration of that
pulse; during this time the TR (for transmit-receive) switch connects
the transmitter r-f line to the antenna, and disconnects the mixer and the
rest of the radar receiver shown below the TR switch. The ATR (for
anti-TR) switch, when fired, simply permits the r-f pulse from the trans¬
mitter to pass through it with negligible loss. Between pulses, when
these gas-discharge switches are in an unfired state, the TR switch
connects the mixer to the antenna, and the ATR disconnects the magne¬
tron to prevent loss of any part of the feeble received signal.

After passing through these two switches, the transmitter pulse
travels down the r-f line to the antenna, where it is radiated. The

INTRODUCTION

[Sec. 1-4

antenna is designed in such a way that the beam shape it produces is
suitable for the requirements the radar set must meet. It is mounted on
a scanner which is arranged to sweep the beam through space in the
manner desired; simple azimuth rotation is indicated in Fig. 1-4.

After the transmission of the pulse, the discharges in the TR and
ATR switches cease and the system is ready to receive echoes. Echoes
are picked up by the antenna and sent down the r-f line to the mixer.
The mixer is a nonlinear device which, in addition to receiving the signals
from the antenna, is supplied c-w power from a local oscillator operating
at a frequency only a few tens of megacycles per second away from the
magnetron frequency. The difference frequency that results from mixing
these two signals contains the same intelligence as did the original r-f
echoes, but it is at a sufficiently low frequency (typically, 30 Mc/sec) to
be amplified by more or less conventional techniques in the intermediate-
frequency amplifier shown. Output signals from the i-f amplifier are
demodulated by a detector, and the resulting unipolar signals are further
amplified by a video-frequency amplifier similar to those familiar in
television technique.

The output signals of the video amplifier are passed to the indicator,
which displays them, let us say for definiteness, in plan-position form.
In order to do this, it must receive a timing pulse from the modulator, to
indicate the instant at which each of the uniform range sweeps out from
the center of the PPI tube should begin. It must also receive from the
scanner information on the direction in which the antenna is pointing,
in order that the range sweep be executed in the proper direction from the
center of the tube. Connections for accomplishing this are indicated in
the Fig. 1-4.

In Chaps. 9 to 14, inclusive, the detailed design of each of the com¬
ponents shown in Fig. 1-4 is treated. In addition, consideration is given
to the problem of supplying primary power in a form suitable for use with
a radar set; this is especially difficult and important in the case of airborne
radar.

1-4. The Performance of Radar. —In discussing the performance of
radar, one usually refers to its range performance —that is, the maximum
distance at which some target of interest will return a sufficiently strong
signal to be detected. The factors that determine range performance are
numerous and they interact in a rather complicated way. Chapter 2 is
devoted to a discussion of them, and Chap. 3 deals with the important
matter of the properties of radar targets.

The usual inverse-square law which governs the intensity of radiation
from a point source acts to determine the range dependence of the fraction
of the total transmitted energy that falls on a target. So far as the echo
is concerned, the target can also be thought of as a point source of radia-

Sec. 1-4]

THE PERFORMANCE OF RADAR

tion, so that the inverse-square law must be applied again to determine
the range dependence of the amount of echo energy reaching the receiver.
In consequence, the echo energy received from a target varies with the
inverse fourth power of the range from the radar set to the target, other
factors being constant.

To be detectable, a signal must have a certain minimum power; let
us call the minimum detectable signal Sam. Then the maximum range
of a radar set on a target of a given type will be determined by
according to the expression

* _ KPt

Omm — ,

■^mai

where K is a constant and P t is the power in the transmitted pulse, to
which the received signal power will clearly be proportional. Rearranging,

Equation (2) displays the difficulty of increasing the range performance
of a radar set by raising its pulse power. A 16-fold increase in power is
required to double the range.

However formidable this requirement appears, one of the most
remarkable facts of the wartime years of development of radar is that
practicable pulse powers in the microwave frequency range (about 1000
Mc/sec and above) have increased by a factor of hundreds in a relatively
short time. This stupendous advance resulted from the invention and
rapid improvement of the multicavity magnetron, which is described in
Chap. 10. Figure 1-5 shows the history of magnetron development, with
respect to pulse power and efficiency, at the three most important micro-
wave bands exploited during the war. The curves are rather arbitrarily
drawn, and only their general trend is significant. Not every upward

INTRODUCTION

[Sec. 1-4

step in output power was due to an improvement in the magnetron itself.
The increase at 10-cm wavelength in the early part of 1941 was brought
about by the development of modulators of higher power.

It is important to realize that the curves of Fig. 1-5 lie above one
another in the order of increasing wavelength not because development
was begun earlier at 10 cm than at 3 cm, and earlier at 3 cm than at 1 cm,
but because magnetrons of the type used in radar are subject to inherent
limitations on maximum power which are more severe the shorter the
wavelength. The same is true of the r-f transmission lines used at
microwave frequencies. The horizontal dashed lines shown in Fig. T5a
show the maximum power that can be handled in the standard sizes of
“waveguide” used for r-f transmission at the three bands.

A similarly spectacular decrease in the minimum detectable signal,
due to the improvement of microwave radar receivers, has marked the
war years. In the wavelength bands above about 10 m, natural “static”
and man-made interference set a rather high noise level above which
signals must be detected, so that there is little necessity for pursuing the
best possible receiver performance. This is not true at microwave fre¬
quencies. Natural and man-made interference can be neglected at these
frequencies in comparison with the unavoidable inherent noise of the
receiver. This has put a premium on the development of the most
sensitive receivers possible; at the end of 1945 microwave receivers were
within a factor of 10 of theoretically perfect performance. Improvement
by this factor of 10 would increase the range of a radar set only by the
factor 1.8; and further receiver improvement can today be won only by
the most painstaking and difficult attention to details of design.

Why Microwavest —The reader will have observed that when radar is
discussed in what has gone before, microwave radar is assumed. This is
true of the balance of this book as well. So far as the authors of this
book are concerned, the word radar implies not only pulse radar, as has
already been remarked, but microwave pulse radar. Though it is true
that the efforts of the Radiation Laboratory were devoted exclusively to
microwave pulse radar, this attitude is not entirely parochialism. The
fact is that for nearly every purpose served by radar, microwave radar
is preferable. There are a few applications in which longer-wave radar
is equally good, and a very few where long waves are definitely preferable,
but for the overwhelming majority of radar applications microwave radar
is demonstrably far more desirable than radar operating at longer
wavelengths.

The superiority of microwave radar arises largely because of the
desirability of focusing radar energy into sharp beams, so that the direc¬
tion as well as the range of targets can be determined. In conformity
with the well-known laws of physical optics, by which the sharpness of

Sec. 1-4]

THE PERFORMANCE OF RADAR

the beam passing through an aperture of given size depends on the ratio
of the diameter of the aperture to the wavelength of the radiation in the
beam, the sharpness of the beam produced by a radar antenna (which
can be thought of as a sort of aperture for the radio energy) depends on
the ratio of the antenna dimensions to the wavelength used. For an
antenna of given size, the breadth of the beam produced is proportional
to the wavelength. These statements are made precise in Sec. 9-1.

Particularly in the case of airborne radar, where a large antenna
cannot be tolerated for aerodynamic reasons, it is important to produce
sharp radar beams with an antenna structure of modest size. This
demands the use of microwaves. Roughly speaking, microwaves are
radio waves whose wavelength is less than 30 cm.

Radar definition, its ability to discriminate between targets close
together in space, improves as the beamwidth is narrowed. Targets at
the same range can be distinguished by radar as being separate if they
are separated in azimuth by an angle larger than one beamwidth; thus
the quality of the picture afforded by radar improves as the beamwidth
is reduced. For an antenna of given size, the beamwidth can be decreased
only by lowering the wavelength.

The finite velocity of light sets a limit to the desirable beamwidth if
a region of finite size is to be scanned at a given speed by a radar set.
Chapter 4 considers this and other limitations of pulse radar in some
detail.

The Propagation of Microwaves— Further limitations on the perform¬
ance of radar arise from the propagation properties of radio waves in the
microwave region of the electromagnetic spectrum. Like light, micro-
waves are propagated in straight lines. Unlike radio waves at frequencies
lower than about 30 Mc/sec, microwaves are not reflected from the
ionosphere. This means that the maximum range of a radar set whose
performance is not otherwise limited will be set by the optical horizon
which occurs because the earth is round. This is in fact the limitation
on the performance of the best radar Sets developed during the war.
Under certain conditions, bending of the microwave beam around the
earth is produced by meteorological conditions (Sec. 2-14). This can
increase the range of a radar set beyond the optical horizon, but such
phenomena are relatively rare and essentially unpredictable.

A lower limit on the wavelengths which can be used for practical
radar systems is fixed by the onset of atmospheric absorption of micro-
wave energy. Below a wavelength of about 1.9 cm, serious absorption
occurs in moist atmosphere, because of a molecular transition in water
vapor which can be excited by the radiation (Sec. 215). For this reason,
2 cm is about the shortest wavelength at which radar systems of good
range performance can be built. For certain very special applications

INTRODUCTION

[Sec. 1-5

where high absorption can be tolerated or is even welcome, shorter wave¬
lengths can be used, but 2 cm is a good practical limit. The wartime
development of radar components and systems at 1.25 cm antedated the
discovery of the strong water-vapor absorption at this wavelength. A
wavelength of 1.25 cm is, fortuitously, very nearly the most unfortunate
choice that could have been made in the development of a new short-
wavelength band.

1-5. Radar Systems. —The uses made of radar were so various under
wartime conditions that many different systems were developed to fill
different needs. These systems usually differed more in regard to beam
shape, scanning means, and mode of indication than in regard to any
other properties. Chapter 6 gives a brief conspectus of the principal
varieties of radar, with especial emphasis on those types that promise to
have an important peacetime use. Two examples of the detailed design
of radar systems are given in Chap. 15, after the components of radar
systems have been discussed.

Considerable use has been made of radar beacons. These are devices
which, on receiving a pulse or a series of properly coded pulses from a
radar set, will send back in reply a pulse or a series of coded pulses. A
great increase in the flexibility and convenience of the use of radar under
certain conditions can be obtained by the use of such beacons. A brief
account of their properties and uses, though not of their design, will be
found in Chap. 8.

Toward the end of the war, two major developments occurred which
promised to extend greatly the applicability of pulse radar under unfavor¬
able conditions. Means were developed for reproducing radar indications
at a point distant from the set that gathered the original data; the intelli¬
gence necessary was transmitted from the radar to the distant indicator
by radio means. This radar relay, as it has come to be called, is described
in some detail in Chap. 17.

Chapter 16 deals with another important development—namely, the
modification of pulse-radar equipment so that it will display only targets
that are in motion relative to the radar. Such moving-target indication
is potentially of great importance in freeing radar from the limitations of
site. At the present, a radar site must be chosen with careful attention
to the surrounding terrain; hills or buildings within the line of sight can
return strong “permanent echoes” which mask target signals over a large
part of the desirable coverage of the set. In mountainous terrain, this
problem is very serious. An arrangement that gives signals only from
targets that are moving appears to be the best solution to the permanent-
echo problem.

A fact that has been too little recognized when radar systems are
discussed is that the organization which is to make use of the positional

Sec. 1-6]

THE EARLY HISTORY OF RADAR

information afforded by radar is usually at least as important as is the
radar itself. A good organization can make excellent use even of inferior
radar information, as was proved by the success of the British Home
Chain of radar stations, the first large-scale radar installation to be made.
An inadequate organizational set-up can do a poor job, even though
provided with splendid radar from the technical standpoint. The many
problems that enter into the creation of an adequate organization for the
use of radar data have not received the study that they should. Despite
this fact, Chap. 7 attempts to provide an introduction to this sort of
planning, and to raise some of the important problems, even though they
may not yet be satisfactorily solved.

1-6. The Early History of Radar. —Though the complete history of
the origins and the growth of modern radar is a long and complicated one, 1
it will be of some interest to sketch here its main lines, with especial
reference to Allied developments.

Successful pulse radar systems were developed independently in
America, England, France, and Germany during the latter 1930’s. Back
of their development lay half a century of radio development for commu¬
nication purposes, and a handful of early suggestions that, since radio
waves are known to be reflected by objects whose size is of the order of a
wavelength, they might be used to detect objects in fog or darkness.

The fact that radio waves have optical properties identical with those
associated with ordinary visible light was established by Heinrich Hertz
in 1886, in the famous series of experiments in which he first discovered
radio waves. Hertz showed, among other things, that radio waves were
reflected from solid objects. In 1904 a German engineer, Hulsmeyer,
was granted a patent in several countries on a proposed way of using
this property in an obstacle detector and navigational aid for ships. In
June 1922, Marconi strongly urged the use of short waves for radio
detection.

The principle of pulse ranging which characterizes modern radar was
first used in 1925 by Breit and Tuve, of the Carnegie Institution of Washing¬
ton, for measuring the height of the ionosphere. 2 After the successful
experiments of Breit and Tuve, the radio-pulse echo technique became the
established method for ionospheric investigation in all countries. The
step from this technique to the notion of using it for the detection of air¬
craft and ships is, in retrospect, not such a great one; and various indi¬
viduals took it independently and almost simultaneously in Aunerica,

1 For the fullest treatment of radar history available, the reader is referred to the
official history of Div. 14, NDRC, “ Radar ” by H. E. Guerlac, to be published by
Little, Brown, & Co., Boston.

5 M. A. Tuve and G. Breit, “Terrestrial Magnetism and Atmospheric Electricity,”
Vol. 30, March-December 1925, pp. 15-16. Also Phys Rev, 28, 554 (1926).

INTRODUCTION

[Sec. 1-6

England, France, and Germany, about ten years after the original work
of Breit and Tuve.

The research agencies of the American Army and Navy have a long and
complicated history of early experiment, total failure, and qualified suc¬
cess in the field of radio detection. The interested reader will find this
dealt with at length in Dr. Guerlac’s history. 1 Here it will be sufficient
to report the earliest full successes. In early 1939, a radar set designed
and built at the Naval Research Laboratory was given exhaustive
tests at sea during battle maneuvers, installed on the U.S.S. New York.
The first contract for the commercial manufacture of radar equipment
was let as a result of these tests, for the construction of six sets, designated
as CXAM (Sec. 6-9), duplicating that used in the trials. In November
1938, a radar position-finding equipment intended for the control of
antiaircraft guns and searchlights, designed and built by the Signal Corps
Laboratories of the Army, was given extensive tests by the Coast Artillery
Board, representing the using arm. This set also went into quantity
manufacture, as the SCR-268 (Sec. 6T4). An Army long-range aircraft-
detection set whose development had been requested earlier by the Air
Corps was demonstrated to the Secretary of War by the Signal Corps
Laboratories in November 1939. A contract for the production of this
equipment, the SCR-270 (and SCR-271; see Sec. 6-9) was let in August
1940.

British radar was developed at about the same time but its application
proceeded at a somewhat faster pace under the immediate threat to
England and with considerably greater realism during the early years of
the war. During the winter of 1934-1935, the Air Ministry set up a Com¬
mittee for the Scientific Survey of Air Defense. Among the suggestions
it received was a carefully worked out plan for the detection of aircraft
by a pulse method, submitted by a Scottish physicist, now Sir Robert
Watson-Watt, then at the head of the Radio Department of the National
Physical Laboratory.

The first experimental radar system of the type suggested by Watson-
Watt was set up in the late spring of 1935 on a small island off the east
coast of England. Development work during the summer led to the
blocking-out of the main features of the British Home Chain of early-
warning stations (Sec. 6-9) by fall. Work began in 1936 toward setting
up five stations, about 25 miles apart, to protect the Thames estuary.
By March 1938, all these stations—the nucleus of the final Chain—were
complete and in operation under the charge of RAF personnel.

British radar development effort was then brought to bear on airborne
radar equipment. Two types were envisaged: a set for the detection of
surface vessels by patrol aircraft (called ASV, for air to surface t’essel),

1 Op. cit.

Sec. 1-7)

WARTIME RADAR DEVELOPMENT

and an equipment for enabling night fighters to home on enemy aircraft
(called AI, for aircraft interception). Work was concentrated on ASV
first, and an experimental equipment was successfully demonstrated
during fleet maneuvers in September 1938. Experimental AI equipment
was working by June, 1939. and it was demonstrated to the chief of RAF
Fighter Command in August of that year. The Air Ministry asked that
30 such systems be installed in aircraft in the next 30 days. Before the
end of September all these systems had been installed, four having been
ready on the day war broke out.

Emphasis on airborne radar underlined the point that, if sharp radar
beams were ever to be produced by antennas small enough to carry in an
airplane, wavelengths shorter than the l£ m used in early British air¬
borne equipment would have to be employed. This led to the effort
that the British put into developing a generator of microwaves which
could give pulse power adequate for radar use. By early 1940, a British
version of the multicavity magnetron had been developed to the point
where it was an entirely practicable source of pulsed microwave energy,
and the history of modern radar had begun.

1*7. Wartime Radar Development in the United States.—Before the
end of 1940, the work on radar of American and British laboratories had
been combined as a result of an agreement between the two governments for
exchange of technical information of a military nature. A British Technical
Mission arrived in Washington in September 1940 and mutual disclosures
were made of British and American accomplishments in radar up to that
time. Members of the British mission visited the Naval Research
Laboratory, the Army Signal Corps Laboratories at Fort Monmouth,
and the Aircraft Radio Laboratory at Wright Field, as well as manufac¬
turing establishments engaged in radar work. They demonstrated their
version of the cavity magnetron and furnished design information that
enabled U. S. manufacturers to duplicate it promptly.

In discussions with the Microwave Committee of the National
Defense Research Committee, which had been set up a few months before,
members of the British Mission proposed two specific projects which
they suggested that the United States undertake: a microwave aircraft-
interception equipment, and a microwave position finder for antiaircraft
fire control.

To implement their decision to follow these suggestions, the Micro¬
wave Committee of the NDRC decided to set up a development labora¬
tory staffed primarily by physicists from a number of universities.
They were encouraged in this step by the success that the British had
already experienced with civilian wartime radar development agencies
staffed with physicists having no special radio experience but good
general scientific training. After exploring several possibilities, the

INTRODUCTION

[Sec. 1-7

Microwave Committee persuaded the Massachusetts Institute of Tech¬
nology to accept the responsibility of administering the new laboratory.
The Radiation Laboratory, as it was named, opened its doors early in
November 1940. The director of the laboratory throughout its 62
months of life was Dr. L. A. DuBridge.

The Army and Navy development laboratories were glad to depend
on the new Radiation Laboratory for an investigation of the usefulness
for radar of the new microwave region of the radio spectrum. They were
fully occupied with the urgent engineering, training, and installation
problems involved in getting radar equipment that had already been
developed out into actual military and naval service. At the end of
1940, the use of microwaves for radar purposes seemed highly speculative,
and the Service laboratories quite properly felt it their duty to concentrate
on radar techniques that had already been worked out successfully.

During 1941, while the Navy was installing long-wave search radar
and medium-wavelength fire-control radar on ships of the fleet, and the
Army was sending out Signal Aircraft Warning Battalions equipped with
the SCR-270 and antiaircraft batteries with the SCR-268, not a single
item of radar equipment based on the new microwave techniques was
delivered for operational use. However, development work at the
Radiation Laboratory had broadened far beyond the two specific projects
suggested by the British Technical Mission, and microwave equipment
was showing great promise for many wartime uses.

A few important dates will indicate the way in which this develop¬
ment was proceeding. On Jan. 4, 1941, the Radiation Laboratory’s first
microwave radar echoes were obtained. A successful flight test of a
working “breadboard” model of an airborne radar intended for AI use
was made on March 10, in a B-18A furnished by the Army Air Corps.
In this flight it was found that the equipment was extremely effective in
searching for ships and surfaced submarines at sea.

In the late spring of 1941, an experimental microwave sea-search
radar equipped with a PPI was installed on the old destroyer U.S.S.
Semmes. On June 30, the Navy let the first production contract for
microwave radar equipment based on the work of the Radiation Labora¬
tory. This was for a production version of the set that had been demon¬
strated on the Semmes.

At the end of May, a prototype of the microwave antiaircraft position
finder developed at the Radiation Laboratory was in operation. It
accomplished the then-astonishing feat of tracking a target plane in
azimuth and elevation wholly automatically.

These and other early successes led to an increasing Service interest in
microwave radar, which had seemed so speculative a venture in 1940.
The tremendous expansion of the development program can be measured

Sec. 1-7]

WARTIME RADAR DEVELOPMENT

by the fact that the personnel of the Radiation Laboratory, which had
been about 40 at the beginning of 1941, rose to nearly 4000 by mid-1945.
Similarly, the Radar Section of the Naval Research Laboratory increased
its personnel to 600. The Radio Position Finding section of the Signal
Corps Laboratories grew into the Evans Signal Laboratory, with a peak
personnel of more than 3000. A similar growth took place at the Air¬
craft Radio Laboratory at Wright Field.

A tremendous amount of work was carried out during the war by the
research and engineering staffs of many industrial concerns, both large
and small. In some cases, these firms, working either independently
or on development or production contracts with the armed forces or with
NDRC, engineered certain types of radar sets all the way through from
the basic idea to the finished product. To a larger extent, the contribu¬
tion of industry was to take the prototype equipment produced in
government laboratories and make the design suitable for quantity
manufacture and for service use Under combat conditions. The art
advanced so rapidly in the early years that manufacturers were often
called upon to make major changes during the course of production in
order to take account of new lessons from both the laboratories and the
battlefields.

The growth of the radar industry, which scarcely existed before 1940,
is indicated by the fact that by the end of June 1945, approximately
$2,700,000,000 worth of radar equipment had been delivered to the Army
and the Navy. At the end of the war, radar equipment was being
produced at a rate of more than $100,000,000 worth per month.

The enormous wartime investment of money, skill, and productive
facilities in radar paid the Allies handsome dividends with the fleet, in the
air, and on the battlefield. 1 The uses of radar in a peaceful world were
just- beginning to be worked out in 1946. Some of these are dealt with
in Vol. 2 of this series. But the technical achievement represented by
the wartime development of radar seems very nearly unparalleled. In
terms of the time intervening between the reception of the first radar
signals and the large-scale use of radar in the war, it is as if, seven years
after the first faltering flight of the Wright brothers at Kitty Hawk, the
airplane had been developed into a powerful weapon of which thousands
were in constant use.

1 The story of radar’s operational use in the war is told, in a way that is somewhat
blurred about the edges by the censorship obtaining just before the end of the war
with Japan, in a pamphlet entitled "Radar: A Report on Science at War,” released
by the Joint Board on Scientific Information Policy on Aug. 15, 1945. It is obtain¬
able from the Superintendent of Documents, U.S. Government Printing Office,
Washington, D.C.

CHAPTER 2

THE RADAR EQUATION

By E. M. Purcell

The operation of a radar set depends on the detection of a weak
signal returned from a distant reflecting object. The factors which
control the strength of the signal so received are clearly of first importance
in determining the maximum range of detection of a given target by a
specified radar set. In Secs. 21 to 2-6 we shall formulate and examine
the basic relation between these quantities, which is commonly known
as the “radar equation.” Specifically, we want to derive an expression
for the peak radio-frequency signal power S, available at the terminals
of the radar antenna, which will involve measurable properties of the
transmitting and receiving antenna system, the transmission path
through space, and the target itself. Now this relation will not suffice
to fix the maximum range of detection unless the minimum power
required for detection, i$Ln, is known. This important quantity S mix , we
prefer to discuss separately, beginning in Sec. 2-7 below. It will be found
to depend on many other factors, not all readily accessible to measure¬
ment, ranging from thermal noise in a resistor to the integrating property
of the eye of the radar observer. Thus we choose to divide the problem
into two parts, by a fictitious boundary, as it were, between the radar
antenna and the rest of the set. The relations which we shall develop
in Secs. 2T to 2-6 are wholly geometrical ones in the sense that the factors
upon which the received power S depends are all lengths, apart from the
transmitted power P, to which, of course, S is always proportional.

THE RADAR EQUATION FOR FREE-SPACE PROPAGATION

2-1. The Meaning of Free-space Propagation. —Fortunately, the
quasi-optical nature of microwave propagation permits us to concentrate
our attention at the outset on a very simple case, which we shall call
“free-space propagation.” The circumstances implied would be realized
exactly if radar set and target were isolated in unbounded empty space.
They are realized well enough for practical purposes if the following
conditions are fulfilled:

1. No large obstacles intervene between antenna and target, along
an optical line of sight.

Sec. 2-2] ANTENNA GAIN AND RECEIVING CROSS SECTION 1 9

2. No alternate transmission path, via a reflecting surface, can be
followed by a substantial fraction of the radiated energy.

3. The intervening atmosphere is homogeneous with respect to index
of refraction, at the frequency used.

4. The intervening atmosphere is transparent, i.e., does not absorb
energy from the wave, at the frequency used.

Condition 1 restricts our attention to targets within the horizon.
Condition 2 bars, for the present, consideration of radar search at low
angles over water, although later we shall include this case by a suitable
modification of the radar equation. Microwave radar over land appears
to be relatively free, even at low angles, from the reflection effects which
are so pronounced at longer wavelengths. In any case, if the directivity
of the antenna pattern is such that very little energy strikes the reflecting
surface, Condition 2 is fulfilled. Any implications of Conditions 3 and 4
which are not self-evident will be clarified in the last part of this chapter,
where other types of propagation will be discussed. If, now, these condi¬
tions of free-space propagation apply, the result is very simple: The
transmitted wave, at any considerable distance from the antenna, 1 has
spherical wavefronts—limited in extent,- of course, by the radiation
pattern of the antenna—which spread so that the intensity of the dis¬
turbance falls off with the inverse square of the distance.

2-2. Antenna Gain and Receiving Cross Section.— If the transmitting
antenna were to radiate energy isotropically—that is, uniformly in all
directions—the power flow through unit area at a distance R from the
antenna could be found by dividing P, the total radiated power, by
4ir R 2 . A directive antenna, however, will concentrate the energy in
certain directions. The power flow observed at some distant point will
differ by some factor G from that which would be produced by an antenna
radiating isotropically the same total power. This factor G is called the
“gain” of the antenna in the direction in question. By our definition,
the gain of the hypothetical isotropic radiator is 1 in every direction. For
any other antenna G will be greater than 1 in some directions and less
than 1 in others. It is clear that G could not be greater than 1 in every
direction, and in fact the average of G taken over the whole sphere must
be just 1.

Usually we are interested in antennas for which G has a very pro¬
nounced maximum in one direction, that is to say, antennas which

1 The limitation implied is to distances greater than d 2 /X, where d is the width of
the antenna aperture and X the wavelength. At distances R less than this (less than
360 ft, for example, for X = 3 cm, d = 6 ft), the intensity does not fall off as l/R 2 .
Although this region has been until now of no interest for radar applications, one can
anticipate the development of short-range, very-high-resolution radar for which the
near zone, so defined, will be.of primary importance.

THE RADAR EQUATION

[Sec. 2-2

radiate a well-defined beam. This maximum value of G we shall denote
by Go. The narrow, concentrated beams which are characteristic of
microwave radar require, for their formation, antennas large compared
to a wavelength. In nearly every case the radiating system amounts to
an aperture of large area over which a substantially plane wave is excited.
For such a system, a fundamental relation connects the maximum gain
Go, the area of the aperture A, and the wavelength:

4tt Af
X 2

( 1 )

The dimensionless factor / is equal to 1 if the excitation is uniform in
phase and intensity over the whole aperture; in actual antennas/is often
as large as 0.6 or 0.7 and is rarely less than 0.5. An antenna formed by a
paraboloidal mirror 100 cm in diameter, for a wavelength of 10 cm,
would have a gain of 986 according to Eq. (1) with / = 1, and in practice
might be designed to attain Go = 640.

The connection between gain and beamwidth is easily seen. Using
an aperture of dimensions d in both directions, a beam may be formed
whose angular width, 1 determined by diffraction, is about \/d radians.
The radiated power is then mainly concentrated in a solid angle of X 2 /d 2 .
An isotropic radiator would spread the same power over a solid angle
of 471-. Therefore, we expect the gain to be approximately 4«f 2 /X 2 , which
is consistent with Eq. (1), since the area of the aperture is about d 2 . For
a more rigorous discussion of these questions the reader is referred to
Vol. 12, Chap. 5.

A complementary property of an antenna which is of importance
equal to that of the gain is the effective receiving cross section. This
quantity has the dimensions of an area, and when multiplied by the power
density (power per unit area) of an incident plane wave yields the total
signal power available at the terminals of the antenna. The effective
receiving cross section A, is related to the gain as follows:

A, =

GX 2

4jt

( 2 )

Note that G, not Go, has been written in Eq. (2), the applicability of
which is not restricted to the direction of maximum gain or to beams of
any special shape. Once the gain of the antenna in a particular direction
is specified, its effective receiving cross section for plane waves incident
from that direction is fixed. Equation (2) can be based rigorously on the
Reciprocity Theorem (see Vol. 12, Chap. 1). Comparing Eqs. (2) and
(1) we observe that, if the factor/ is unity, the effective receiving cross

1 Wherever a precise definition of beamwidth is intended, we shall mean the
angular interval between two directions for which G = Go/2.

Sec. 2-4]

THE RADAR EQUATION

section of an antenna in the principal direction is precisely the area of
the aperture; in other words, all the energy incident on the aperture is
absorbed. Quite generally A r will depend on the area of the antenna
aperture and not on X, whereas G 0 will depend on A/X 2 .

2-3. Scattering Cross Section of the Target. —We have to consider
how the target itself enters the radar problem. Evidently we need some
measure of the amount of power reflected by the target. For this
purpose we define the scattering cross section of the target u as follows:
<r (dimensions of an area) is to be 4ir times the ratio of the power per unit
solid angle scattered back toward the transmitter, to the power density
(power per unit area) in the wave incident on the target. In other
words, if at the target the power incident on an area a placed normal
to the beam were to be scattered uniformly in all directions, the intensity
of the signal received back at the radar set would be just what it is in the
case of the actual target. In some respects “radar cross section” is a
more appropriate name for a in so far as it indicates that we are concerned
only with the power scattered directly back toward the transmitter.

It is essential to realize that the cross section of a given target will
depend not only upon the wavelength but upon the angle from which the
target is viewed by the radar. The fluctuation of a with “target aspect,”
as it is called, is due to the interference of reflected waves from various
parts of the target (see Chap. 3). Only for certain special cases can a be
calculated rigorously; for most targets a has to be inferred from the radar
data themselves. Usually this cannot be done in any uniform way
because of the fluctuation referred to, and it may be well to assert at this
point that intelligent use of the formulas which we shall derive, in all of
which <7 appears, requires an appreciation of these limitations.

2'4. The Radar Equation. —With the pertinent quantities defined it is
now a simple matter to formulate the radar equation. If S is the signal
power received, P the transmitted power, G the gain of the antenna, X the
wavelength, a the radar cross section of the target, and R the distance
to the target or range, this relation must hold:

s -(S)(i^)Cl’) < 3 «>

The quantity in the first parenthesis is the power density in the incident
wave at the target. The first two terms in parentheses together give the
power density in the returning wave at the radar antenna, and the last
factor will be recognized as the receiving cross section of the radar
antenna, from Eq. (2). Rearranging terms, for compactness,

<? 2 XV
(4ir ) 3 E 4 '

S = P

(36)

THE RADAR EQUATION

[Sec. 2-5

Again we call attention to the fact that Eq. (36), like Eq. (2), contains G
rather than Go, and is not restricted to any particular direction or to
beams of any special shape. The sole restriction which has not yet been
made explicit is that G should not vary significantly over the angle which
the target subtends at the radar antenna.

Usually we shall be interested in the signal that is returned when the
target lies somewhere along the maximum of the radar beam, and we
should then replace G by C?o. It is instructive to proceed then to elimi¬
nate Go by means of Eq. (1), obtaining

Pa A Y-
4 ttE 4 X 2 '

(4a)

Note that X 2 now appears in the denominator, while the numerator con¬
tains the square of the area of the antenna aperture. A further manipu¬
lation of Eq. (4a) is of interest. Suppose the minimum power required
for satisfactory detection, is known; we may solve Eq. (4a) for the
maximum range of detection,

„ *lPeA*P

Rm " ~ (46)

At this point it may be well to get an idea of the order of magnitude
of the quantities involved by inserting numbers not unusual in wartime
pulse-radar practice. If we choose X = 0.10 ft (= 3.0 cm), P = 10 6
watts, A — 10 ft 2 , / = 0.6, a = 100 ft 2 (typical for small aircraft),
jSm-u> = 5 X 10 -12 watts, we obtain = 155,000 ft or 29 statute miles.

We observe that a 16-fold increase in transmitted power is required to
double the maximum range; on the other hand, it would appear that
could be doubled by doubling the linear dimensions of the antenna. But
the latter step would at the same time reduce the beamwidth by a factor
of 2 and as we shall see in Sec. 2-11 that this indirectly affects A

change in wavelength is even more difficult to discuss as it entails changes
in /Smin, P, and possibly a as well.

2-6. Beams of Special Shapes. —In several applications of radar, use
is made of an antenna designed to spread the radiated energy out over a
considerable range in angle in one plane. The object usually is to
increase the angular region covered at one time. An example of such a
radiation pattern is the simple “fan beam” sketched in Fig. 2T. It is
easy to produce such a beam by means of an antenna whose effective
aperture is wide in the direction in which the beam is to be narrow and
narrow in the direction in which the beam is to be broad. The con¬
nection given by Eq. (1) between aperture and gain still holds, implying
that by reducing the vertical dimension of the antenna aperture (in
Fig. 2T), gain has necessarily been sacrificed; of course this is inevitable,

Sec. 2-5]

BEAMS OF SPECIAL SHAPES

for the radiated energy has been spread out over a large solid angle.
Consider the problem of designing a radar set with the requirement
imposed that the vertical beamwidth be 13. Let us recast Eq. (4) in a
form appropriate for this case, introducing explicitly the vertical and
horizontal dimensions of the antenna aperture, which we denote by b
and a respectively. To a good enough approximation we can set b — \/@.
Then A 2 = a-b' 1 = a 2 X 2 //3 2 , and inserting this in Eq. (4b) we have

7 :

Perf 2 a 2

4ir<S mi n/3 2

(5)

The range no longer depends explicitly on the wavelength.

From what has been said it should be clear that an excess of antenna
gain, in any direction, over what is needed to meet any requirement for

detecting targets in that direction is wasteful. It would be most desirable
to adjust the directional pattern of the antenna so that just the desired
angular coverage, and no more, would be obtained. A prescription for
such an antenna pattern can be obtained from the basic radar equation,
Eq. (3b), in any given case. A particularly important and instructive
example is that of airborne ground-mapping radar, which we shall now
examine in detail.

The object here is to obtain a radar picture, from above, of a circular
area on the ground stretching out in all directions from the aircraft to
some maximum range Ro. This is done by illuminating, at any one

THE RADAR EQUATION

[Sec. 2-5

time, a narrow radial strip extending outward from, for example, the
point directly beneath the aircraft and rotating or “scanning” this strip
about a vertical axis (see Fig. 2-2). Evidently some sort of fan beam, as
narrow as possible in the horizontal direction but spread out vertically, is
demanded. To find the shape which the beam should have, in a vertical
plane, the properties of the target must be taken into account. Unlike
the targets previously discussed, which were assumed to be small com¬
pared to the cross section of the beam and to be characterized by a fixed
radar cross section a, the ground is an extended, or compound target. It
consists of a multitude of small scattering or reflecting objects, many of

which contribute to the echo received at any instant. It is easy to see
that the area of the patch on the ground, such as C in Fig. 2-2, from which
echoes can be received at one instant is proportional to the width of the
radar beam at the range in question and to the pulse duration. Also, the
effectiveness of such a patch undoubtedly depends on the angle from
which it is viewed. A detailed discussion of this matter must be reserved
for Chap. 3, but the foregoing remarks should make plausible the follow¬
ing hypothesis:

a — LRa sin 9, (6a)

in which a is the beamwidth in azimuth and L is a factor having the
dimensions of a length that contains the pulse length and otherwise
depends only on the characteristics of the terrain. The factor sin 8

Sec. 2-5]

BEAMS OF SPECIAL SHAPES

expresses well enough for our purposes the effect of viewing the echoing
area obliquely, at least when 0 is small. (In Fig. 2 2 the vertical angles
have been exaggerated, for clarity.)

Substitution of this expression for a in the radar equation, and the
replacement of R by A/sin 0, h being the height of the aircraft, leads to

„ „ (j 2 XV P\ 2 LaG 2 sin 4 0 ....

S = p (4 WR i = — W- (6b)

If S is to be independent of 0 between 0 = 0 O and 0 = ir/2, we must
require that (7(0) vary as esc 2 0 through this angular interval. The ideal
antenna pattern then would be described by

G = G,

CSC 2 0

esc 2 0o

G = 0, at all other angles.

for 0 O < 0 < ir/2,

(7)

The requirement of Eq. (7) imposes a restriction on the maximum
gain Go which can be achieved and hence on the maximum range. To see
this, let us compute the average of the gain of the antenna over all
directions, or l/4ir f fG dui extended over the whole sphere, where dw is the
element of solid angle. By the definition of gain this integral must be
equal to 1. But first something must be said about the shape of the
antenna pattern in the other plane—that is, in a plane normal to the fan
beam. Suppose that the horizontal width of the antenna aperture has
been fixed by other design considerations at the value a. The maximum
gain possible will be obtained if the illumination of the antenna aperture
is uniform horizontally, and in this case it can be shown that in any
plane such as ACEF, Fig. 2-2, the gain as a function of the angle 4>
will be 1

G* — G td,=o

, {ira<f>\

V \)

/ ira,<j>

\T.

(8)

)

As a function of 0 and 4> then, the pattern is completely described by

G — Go

CSC 2 0
CSC 2 00

'-(?)
(”*)' ’

(9)

and we have to require

j p' r + 2

4r Jo J -l

G cos 4> d<t> dd — 1. Since G is very

1 This expression will be recognized as the diffraction pattern of a rectangular
aperture. See Vol. 12, Sec. 4-9.

THE RADAR EQUATION

[Sec. 2-5

small except for small values of <#>, and since G vanishes for values of 6
outside the interval 6 0 to ir/2, it is permissible to write and evaluate the
integral as follows;

1 Go
4ir esc 2 do

Hence

4ira

sec do esc do,

or from Eq. (7)

G =

4ira

tan 8 o esc 2 8.

( 10 )

(ID

Returning now to Eq. (6b), if G is replaced by the right-hand side of
Eq. (11), and a replaced by X/o, we obtain, for S,

S =

PLa\ tan 2 8 0
Airh 3

( 12 )

When do is small, as is usually the case, it is permissible to replace h /tan d 0
by Rw .«, the maximum range, which leads to the final relation

PLdK

4irbftL*

(13)

The appearance of X in this formula, which is to be contrasted with
the result obtained for the simple fan beam and point target, Eq. (5), can
be traced to the influence of the horizontal beamwidth upon the effective
cross section of the extended target. It will be observed that once the
other system parameters, P, »S' min , and a, are specified, the quantity
hR 2 is fixed. That is to say, the maximum range obtainable is inversely
proportional to the square root of the height of the aircraft, keeping
everything about the radar set constant but the vertical radiation
pattern of the antenna, which we assume to be adjusted to optimum
shape for each height.

A problem related to the preceding one is met in the design of ground-
based air-search radar, which may be required to provide uniform cover¬
age at all ranges for point targets (aircraft) flying at some limiting
altitude h. Here, however, a is generally assumed to be constant: the
reader will easily verify that this assumption leads again to the require¬
ment that the gain vary as esc 2 8, but with a different final result for the
dependence of S upon h, R, and a. It turns out in fact that for the point
target with a independent of angle, the quantity hRmn is constant, rather
than bR 2 ,,,, and S is proportional to a 2 rather than to aX.

Sue. 2-6]

THE BEACON EQUATION

In practice it is not feasible to produce a pattern which exactly meets
the specification of Eq. (7) but a reasonable approximation has been
achieved in several instances. A comprehensive discussion of the
problem of the “cosecant-squared” antenna, as this type has been
called, will be found in Chap. 14 of Vol. 12.

26. The Beacon Equation. —So far we have confined our attention to
the “two-way” radar problem, in which the route from transmitter to
receiver is a complete round trip involving scattering of the energy by
some remote object. Radar beacons operate on a different principle. A
receiving antenna at a remote point picks up directly energy sent out
from the radar transmitter. The signal is amplified and enabled to
initiate the transmission of another signal, in reply, by an associated
transmitter. This signal, received back at the radar, provides an
artificial echo which can be utilized in various ways (Chap. 8). Here
the analogue of the radar equation for radar-beacon operation will be
discussed.

It is clear that we have to do with two entirely independent processes,
each of which consists simply of one-way transmission and reception.
Consider the first process, usually called “interrogation.” Let P T be the
power transmitted by the radar, Si, the signal power received by the
beacon antenna. These must be related by

s ‘- p '(n§f) (14)

where G r and G b are the gains of the radar and beacon antennas respec¬
tively. The subsequent process of beacon reply is described by a similar
equation with the subscripts b and r interchanged throughout. If the
same antenna or similar antennas are employed for transmission and
reception at the beacon and likewise at the radar, as is nearly always the
case, the quantity in the parenthesis has the same value for interrogation
and reply, and we can infer the corollary relation

St Pr
S r P 6 '

(15)

In practice, the gain G b of the beacon antenna is fixed at a relatively
low number by the requirement of something like omnidirectional cover¬
age. The remaining factor in the parenthesis in Eq. (14) is the quantity
G,X 2 which is proportional to the aperture of the radar antenna. This
leads one to suspect that long beacon ranges should be, in general, more
difficult to achieve at shorter wavelengths. Antenna apertures are
rarely increased in area when shorter wavelengths are employed: on the
other hand, available r-f power generally decreases markedly with
decreasing wavelength. Actually this has not proved to be a serious

THE RADAR EQUATION

[Sec. 2-7

limitation down to wavelengths of the order of 3 cm, because ranges that
can be achieved are already very great and are limited usually by the
horizon rather than by the relation expressed in Eq. (14). That is to
say, the condition of free-space propagation, which we have assumed in
this section, often does not apply at the extremity of the microwave-
beacon range.

Long beacon ranges are, of course, a result of the enormous advantage
of one-way over two-way transmission. If we compare Eq. (14) with
Eq. (4), we see that in signal strength for given transmitted power the
beacon process enjoys the advantage of a factor of AirGbR^/Gjr. It is
interesting to compute the limiting free-space range for a beacon oper¬
ating in conjunction with a radar set of the characteristics assumed in
our earlier radar example. Let us suppose that the gain of the beacon
antenna is 10, and that the transmitted power and minimum required
signal power for the beacon are the same as those assumed for the radar
set. Using Eq. (14) we obtain for the maximum range, either for inter¬
rogation or reply, 60,000 statute miles.

In conclusion, we may point out that Eq. (14), although it has been
written in notation appropriate to the radar-beacon problem, applies, of
course, to any one-way transmission problem where free-space propaga¬
tion can be assumed. Applications of Eq. (14) are to be found in
the fields of microwave radar relay, radar jamming, and microwave
communication.

THE MINIMUM DETECTABLE SIGNAL

2-7. Noise.—It is well known that despite our ability to amplify
a feeble electrical signal by practically any desired factor, it is still not
possible to discern an arbitrarily weak signal because of the presence of
random electrical fluctuations, or “noise.” If the true signal entering
any receiver is made weaker and weaker, it subsides eventually into the
fluctuating background of noise and is lost. What is the origin of these
fluctuations, and what factors determine precisely the level at which
the radar signal is hopelessly obscured by them?

Before we attempt to answer these decisive questions, it is worth
while to consider briefly the limit of useful sensitivity of an ordinary
low-frequency radio receiver. This limit is also set by random dis¬
turbances, but in this case the largest random disturbances with which
the signal must compete originate generally not in the receiver itself
but elsewhere in space. Whatever their source—and this may range
from a passing trolley car to the mysterious reaches of interstellar
space—these disturbances enter the receiver by way of the antenna.
The crucial quantity is therefore the ratio of the field strength of the
signal in the neighborhood of the antenna to that of noise or interference.

Sec. 2-7]

NOISE

The absolute magnitudes of signal and interference power available
at the antenna terminals are of little importance; only their ratio, which,
for example, might be favorably altered by the use of a directional
antenna pattern, determines the ultimate performance. This circum¬
stance is perhaps one reason why the effective receiving cross section
of an ordinary radio antenna is a number of little interest and is indeed
rarely discussed in radio engineering texts. More significantly, it
explains why the emphasis in the development of radio receivers has
been mainly on improving discrimination against some of the external
noise (for example, by greater frequency selectivity) rather than on
reduction of noise inherent in the receiver.

The situation is different in the microwave region. Substantially
all the noise originates in the receiver itself, not because microwave
receivers are noisier or more imperfect receivers than low-frequency
receivers—for they are not, as a rule 1 —but because noise and interference
originating outside the receiver are enormously greater at the lower
frequencies. In fact, such noise in the microwave region is almost
wholly negligible in existing receivers. 2 It is the noise that originates
in the receiver itself against which the signal power determined by
Eq. (3) must compete for recognition.

The level of fluctuations in an otherwise quiescent electrical circuit
can be described in many equivalent ways. One description of which
we shall make use is the following. Let R be the real part of the imped¬
ance measured, at frequency /, between two points in a passive electrical
network, all dissipative parts of which are in thermal equilibrium at
absolute temperature T. Then let the voltage e between these two
points be measured by an ideal voltmeter which is capable of indicating,
without disturbing the circuit in any way, the time average of the square
of e, denoted by e 2 , over a small frequency range ®, 3 in the neighborhood
of the frequency f. It will be found that e 2 so defined is given by

e 2 = IRkT ffi, (16)

where k is Boltzmann’s constant (1.38 X 10 -23 joules/degree).

1 Very few low-frequency receivers approach the best modern microwave receivers
in respect to signal-to-noise ratio, despite the fact that it is easier to attain a low noise
figure at low frequencies, other things being equal.

1 Future large-scale exploitation of the microwave bands may change the picture,
although not, perhaps, as much as one might at first suppose. Both the optical nature
of microwave propagation and the vast frequency band available in the microwave
region of the spectrum mitigate mutual interference.

3 We use ® for bandwidth throughout, for uniformity, although it is common
practice, and in some respects preferable, to write Eq. (16) in differential form

= 4RkT df. Where a finite bandwidth is implied, it will suffice for our purposes
in this chapter to suppose that the voltmeter or amplifier in question has a rectangular
pass band of width ® cps.

THE RADAR EQUATION

[Sec. 2-8

Another description that is often useful involves the notion of “avail¬
able power.” Again, let some passive circuit, which we shall call G, be
in thermal equilibrium at the temperature T. If now we connect across
the terminals of C an impedance element Z, itself at absolute zero, the
maximum rate of transfer of energy from C to Z within the frequency
band (B is just k'T(S>. This rate, which is actually attained when Z is
adjusted to be the complex conjugate of the impedance observed between
the terminals of C, we call the “available noise power” from C. If Z is
not at absolute zero, the transfer is not wholly one-sided; and if Z is at
the same temperature as C, the net transfer vanishes, as of course it must.

This law, which has been derived in various forms by Nyquist 1 and
others, is based on the equipartition law of statistical mechanics and not
on any special assumption as to the details of the mechanism responsible
for the observed fluctuations.

Fig. 2’3.—Schematic diagram of an ideal receiving system.

Other sources of noise are to be found in receivers—notably shot
noise in vacuum tubes—which do depend on a special mechanism. These
we do not intend to examine here since our purposes are first to demon¬
strate the fundamental limitations of an ideal receiver, no matter how
constituted, and second, to study the factors that influence the distin-
guishability of the signal in noise of a specified relative level. In the
latter problem it is allowable to lump together thermal noise and noise
from other sources within the receiver only because these other types of
noise share with thermal noise the bandwidth factor <B, and give rise, at
all frequencies of interest to us, to signals of precisely the same character.

2-8. Receivers, Ideal and Real. —Returning to the original problem,
let us consider the rudimentary receiver shown in Fig. 2-3.

For simplicity, we shall assume that the antenna A constitutes a
matched load on the transmission line of characteristic impedance Z, the
latter being terminated at the other end in the resistor BC, whose resis¬
tance R need not be equal to Z. The box D is an ideal amplifier of
bandwidth ffi, equipped with an output meter E, whose reading is propor¬
tional to the mean square voltage e 2 across BC. The bar as before
denotes a time average, or, more explicitly, an average over a time long
compared with 1/®.

1 H. Nyquist, Phys. Rev. 34, 110 (1928). See also Vol. 24 of this series, Chap. 4.

Sec. 2-8]

RECEIVERS, IDEAL AND REAL

We are interested in the magnitude of e 2 in the absence of signal, which
we denote by ej. In order to apply Eq. (16) we must know the resistance
Rbc between B and C. This consists of R in parallel with the impedance
of the line, Z, or what amounts to the same thing in this case, in parallel
with the radiation resistance of the antenna. That is,

- gfy (17'

What temperature is to be associated with the resistance Z? Or to put
a more restricted question, under what circumstances can we say that R
and Z are at the same temperature? Clearly this is the case if all
surroundings of the antenna with which the antenna is capable of exchang¬
ing energy are at the same temperature T as is R. Let us assume for th»
moment that this is so. Then

el = 4 kT(S>. (18)

Now let a signal be received by the antenna, and let S be the available
signal power—that is, the power which would be absorbed by a matched
load (R = Z) at BC. In general, the mean-square signal voltage el
developed across R will be

from which we have

c 4 R 2 Z
(R + zy’

S R
lcT(S> R + Z

(19)

( 20 )

From Eq. (20) we should infer that the most favorable condition
possible is attained by making R infinite, that is, by terminating the
antenna line in an open circuit. In this special case, el/el = S/kT(S>.
The physical interpretation is at once evident; in this case the noise
originates entirely outside the system, arriving at the antenna as radia¬
tion. 1 The available noise power from the external region is kT CB, just
as S is the available signal power.

In practice, however, the antenna is usually not terminated in an open
circuit, for reasons which were ignored when we made our earlier assump¬
tions about the ideal nature of the amplifier D. Without trying to do
justice to this complicated and important problem we shall say only that
when other sources of noise—in particular, noise in the output of the

1 It is interesting to note that this result can be derived directly from the theory of
black-body radiation by assuming (as we have tacitly done already) the antenna to be
enclosed in a region all at temperature T, and making use of the receiving cross section
of the antenna given by Eq, (2).

THE RADAR EQUATION

[Sec. 2-8

first amplifier stage—are taken into account, together with the fact that
the input impedance of microwave receivers is not unlimited, the optimum
value of R turns out to be finite. The condition R = Z is, in fact, not
unusual. This condition, in our ideal system of Fig. 2-3, leads to

- = —— ( 21 )

2kT(S> K ’

A question of fundamental interest, though not as yet of much
practical moment, is the one raised earlier about the temperature to be
assigned to the antenna radiation resistance. This is certainly not in
general the temperature of the metal parts of the antenna. The reader
may correctly surmise, from what has been said, that the effective tem¬
perature of this element of the circuit is that of any surroundings of the
antenna with which the antenna can exchange energy by radiation—that
is to say, it is the temperature (or a suitable average of the temperatures)
of whatever would absorb energy radiated by the antenna as a trans¬
mitter. This has indeed been demonstrated experimentally. It has been
shown 1 that a microwave antenna pointed at the sky receives only a very
small amount of radiation, corresponding to an absolute temperature of
at most a few degrees. If our receivers were very nearly ideal this would
have the practical result of making it much easier to detect aircraft
appearing at high angles of elevation. In the best existing receivers the
reduction in noise output which could be obtained by pointing the antenna
upward would amount to some 10 per cent.

The foregoing somewhat academic discussion of thermal noise would
be inappropriate in this place were it not for two facts. First, microwave
receivers, even as this is written, have been brought so close to the
pinnacle of ideal performance that it is well for the radar engineer to
appreciate the nearness, and the finality, of the goal. Second, thermal
noise, although it is not wholly to blame for the noise background in
microwave receivers, provides a very convenient standard in terms of
which the performance of an actual receiver can be specified.

We shall define, as the over-all noise figure N of a receiver, the ratio of
signal power available from the antenna to AT 7 ®, 2 when the mean noise
power and the signal power are equal as observed at some stage in the
receiver where both have been amplified so highly as to override com¬
pletely any noise introduced by succeeding stages. In framing the defini¬
tion so broadly we have in effect included, under “receiver,” not only the
mixer but all associated r-f circuits. It is well to do so at this stage, for the
analysis of the contribution of each part of the input system to the over-

1 R. H. Dicke, “The Measurement of Thermal Radiation at Microwave Fre¬
quencies,” RL Report No. 787. See also Dicke el ah, Phys. Rev., 70, 340 (1946).

2 In this definition T is customarily, and arbitrarily, taken to be 291°K

Sec. 2-91 RECEIVER BANDWIDTH AND PULSE ENERGY

all noise figure is complicated by many subtle questions which should not
now concern us. By our definition the noise figure N of the ideal system
of Fig. 2-3 is just 2, if the antenna temperature and the temperature of R
are both 291°K. For the open circuit termination, N = 1. Actually,
over-all noise figures of 10 or lower are not now uncommon in the best
microwave receivers. A noise figure of 10 and a bandwidth of 3 Mc/sec,
for example, imply that a signal of 1.2 X 10 -13 watts will be sufficient to
increase the receiver output by an amount equal to the average noise
output.

2-9. Receiver Bandwidth and Pulse Energy. —In all the expressions
for noise power there appears the width of the amplifier pass band, ffi.
Apart from certain technical limitations, this factor is completely at our
disposal, and we must now decide how its value shall be chosen. To do
this we must for the first time in this chapter admit that we are concerned
with the detection of pulses. Suppose that the r-f
signal pulse consists of a wave train with a rectan¬
gular envelope, of duration r seconds. The re¬
sponse of an amplifier (or filter) to such a pulse
depends on the width of its pass band, which is
in effect an inverse measure of the time of response
of the amplifier. If this response time, in order of
magnitude 1/®, is very much longer than r, the
peak output signal power will be proportional to
the square of the bandwidth ® 2 . On the other
hand, if the response of the amplifier is relatively
very fast, the output will quickly reach a level determined solely by the
input power and the gain, and independent of ffi. Thus if we plot peak
output signal power against ®, for constant (during the pulse) input power
a curve like a of Fig. 2-4 will be obtained.

The average noise power, however, is just proportional to ® according
to Eq. (16) and is represented by the line b of Fig. 2-4. We must there¬
fore expect a minimum in the ratio of noise output to peak signal output,
at some value of ® closely related to 1/r. It is not obvious that such a
minimum should represent precisely the best condition for the detection
of the signal. Indeed it would be surprising if any one criterion, appro¬
priate to all of the various methods of final detection that can be used,
could be found. This need not discourage us as it turns out that all such
criteria lead to similar results, and that moreover the minimum is fairly
flat.

Some results obtained by the group headed by J. L. Lawson in their
investigation of signal discernibility are displayed in Fig, 2-5. A simple
range time base, or A-scope, was used; the video bandwidth was so wide
(10 Mc/sec) as to have a negligible influence on the outcome, at least in

Fig. 2-4.—Variation of
output signal power a
and output noise power b
with bandwidth at con¬
stant pulse duration.

THE RADAR EQUATION

[Sec. 2-9

the neighborhood of the minimum. The signal threshold power plotted
in Fig. 2-5 is essentially the signal strength, relative to average noise
power, for which an observer would identify the signal correctly nine out
of ten times. For a more precise definition of the experimental criterion
for threshold signal in these tests, the reader is referred to Vol. 24, Sec.
8-2. Our interest just now is in the position of the minimum of each
curve that is seen to lie near <B = 1.2/r. However, departure from this

Fig. 2-5. —Signal threshold vs. i-f bandwidth for a pulse duration of 1 /isec. The signal
power is measured in units of the noise power, .Vi, within a band 1 Me/sec wide. In these
experiments the video bandwidth was 10 Me/sec, the signal presentation time was 3 sec,
and the length of the pulse on the screen of the A-scope was 1.7 mm.

value by a factor of 2 in either direction increases the minimum discern¬
ible signal power by less than 1 db. The radar designer is inclined to
take advantage of this latitude to set ® somewhat greater than 1.2/r as
this eases the requirement of accurate frequency control. A value of ®
in the neighborhood of 2/r is typical of present practice; there is some
evidence also from controlled experiments on intensity-modulated indi¬
cators (Vol. 24, Chap. 9) which favors this higher value.

The quantity S/kT($>, which has been our primary concern in this
section, can now be rewritten by expressing ffi in terms of r. If, for
simplicity, we require ® = 1/r then S/kT<& becomes Sr/kT. The prod-

Sec. 210 ]

THE STATISTICAL PROBLEM

uct of the received signal power S and the pulse duration r is just the
energy contained in the received signal pulse, while kT is the average
stored energy in a quiescent system with one degree of freedom. That
the ultimate criterion of detectability should involve a comparison of
these two quantities is certainly not surprising. Thus it is always
possible to rewrite the radar equation, Eq. (4b), in which will always
involve kT<S>, in a form containing, explicitly, not the transmitted power
P, but the energy emitted per pulse, Pt. For example, if the pulse
duration r is increased by a factor of 4, peak pulse power being maintained
constant, a 40 per cent increase in maximum range would be expected.
This can be regarded as the result of increasing the total energy in the
transmitted pulse. The pulse energy is a more significant measure of the
usefulness of a transmitter in long-range detection than is the pulse power,
in so far as the choice of pulse length and bandwidth is not restricted by
other considerations.

2T0. The Statistical Problem.—It might seem that we now have
within our grasp a specification for S mia which can be introduced into the
radar equation to yield the maximum range of detection, R„,„. Unfor¬
tunately, it is not so simple as that. Let us summarize what we do know,
once we are provided with the over-all noise figure and bandwidth of the
receiver, the transmitted power, and the geometrical factors in the radar
equation which concern the antenna and the target. We know the ratio
of the amplified signal power to the average value of the amplified noise
power. We are not yet able to say how large this ratio must be before
the signal can be identified with reasonable certainty. The root of the
difficulty is that we have to do with a statistical problem, a game of
chance. The answers will be given as probabilities, and will depend
upon many features of the system by which the signal is presented to the
observer, as well as upon the precise description of the “reasonable
certainty” mentioned above. We approach the problem by examining
first the character of the noise fluctuations.

The output noise power will fluctuate continually and irregularly
above and below its average value, the latter being understood as an
average taken over a time long enough to include very many fluctuations.
An example that is easy to discuss quantitatively is the following.
Suppose that the intermediate frequency amplifier is followed by a square-
law detector and by further (video) amplification in stages whose pass
band is so broad as to introduce no distortion of the signal. The final
output voltage is then a direct measure of the instantaneous power output
of the i-f amplifier. Let this voltage be displayed, as a function of time,
on an oscilloscope. Figure 2-6a shows a typical single trace which might
be obtained in this way. Now in spite of the wildly irregular nature of
the noise voltage, the theory of random processes applied to this case

THE RADAR EQUATION

[Sec. 2-10

(Vol. 24, Chap. 8) leads to certain positive statements. First, the rapid¬
ity of the fluctuations is determined by the bandwidth ffi of the amplifier.
That is to say, in a time short compared with 1/®, it is extremely unlikely
that the output power will change noticeably. 1 On the other hand,
during a time long compared with 1 /ffi, fluctuations will almost certainly
occur, and the value of the power P at the end of such a long time will
bear no systematic relation at all to the value it happened to have at the
beginning. This is a roundabout way of saying that values of P deter¬
mined at times differing by much more than 1/ffi are statistically inde¬
pendent, or, in other words, 1/ffi is a measure of the correlation time of the
fluctuations.

The second statement which can be made concerns the probability
that at some arbitrarily selected instant the output power will be found
to lie between some specified level, P, and P + dP. This probability,
which we shall label W\(P) dP, is given by

TFi(P) dP = ± e p ° dP. (22)

r o

P o is the average power, determined over a long time.

A statement which is easily seen to be equivalent to this is: The prob¬
ability that the power exceeds some specified level P, at an arbitrarily

selected instant, is just e p °. Thus there is always a finite chance of
getting a high noise peak. For example, the probability that at a given
time P is greater than 5Po is e~ 5 or 0.0068. For the discussion that
follows it is convenient to simplify the problem somewhat by dividing
the time base into discrete intervals each 1/ffi long. In Fig. 2-6a we
would have 50 such intervals. The essential features of the noise back¬
ground can then be described by regarding these intervals as independent 2
and associating some one value of P with each. Again Eq. (22) correctly
expresses the probability that the power, in an arbitrary interval, will lie
between P and P + dP.

The task of detecting a signal amid the noise in this simplified case
amounts to selecting an interval which displays so large a value of P
that one is justified in betting that the peak was due to a combination of
signal and noise, and not to noise alone. This should dispose of any hope
that we shall be able to define once and for all the minimum detectable

1 The intermediate frequency itself is assumed to be high compared with ffi, so that
it is permissible to speak of the instantaneous power while actually meaning the power
averaged over one cycle of the intermediate frequency.

2 The intervals so defined are actually not entirely independent, for the output
power is, after all, a continuous function of the time. We are here substituting for a
continuous random process a discrete random process, which is easier to discuss in
elementary terms.

Sec. 2-10]

THE STATISTICAL PROBLEM

signal Smin. One can never be absolutely sure that any observed peak is
not due to a chance noise fluctuation, and one cannot even say how
probable it is that the peak is not due to noise, unless one knows how
probable it is, a priori, that the peak is due to something else—namely,
signal plus noise. Knowledge of the a priori probability of the presence
of signal is possible in controlled experiments such as those described in
Vol. 24, Chap. 8. For example, it might be arranged to present a signal
at a given point on the oscilloscope sweep about half the time, the observer
being required to judge whether or not the signal was there. A shrewd
observer would call “Signal” whenever the scope deflection at this point
was only a little greater than average, and could score a pretty good
“batting average” even for rather weak signals. If, however, he
expected the signal to occur only very rarely, he would naturally set his
standard higher, in order to avoid frequent false identification of what
were, in fact, noise fluctuations.

For obvious reasons, no such clear delineation of the statistical prob¬
lem is possible in the normal operation of a radar set. However, we can
roughly distinguish different orders of what was called above the a priori
probability of the signal. Compare, for example, the use of a radar set
for early warning (detection of enemy aircraft at a great distance) and
for ground control of aircraft, in which a selected plane, already picked
up on the radar, is followed, its position being noted in each scan. In the
latter case, we know about where to look for the echo in a given scan,
having observed the position in the previous scan and knowing approxi¬
mately the course and speed from still earlier information. Hence, we
accept even a weak indication of the presence of signal if it comes near
the expected place, with comparatively small chance of error. In the
former case, however, a large area of the radar scope must be kept under
surveillance for a long time. The likelihood that a high noise peak will
be observed is much greater: only a very pronounced peak can now be
confidently identified as a new signal.

We have divided our time base into intervals 1/® long. In one
second than, ® intervals come under observation. If ffl is 2 Mc/sec, for
example, this amounts to 2,000,000 intervals per sec. According to Eq.
(22) we expect to find among these some hundred that represent noise
peaks greater than 10P 0 . In one hour there is better than an even chance
of observing one noise peak greater than 20Po. Must we therefore
require that to be detectable a single signal pulse be at least greater than
20Po, or at the terminals of the antenna, greater than 20 NkTS,?

We should indeed, if we are speaking of a single signal pulse. But
anyone who has had anything to do with the design or operation of a
radar set will perceive at once that an essential part of the problem has
so far been ignored. The fact is that detection of a target by radar

Power Power Power

THE RADAR EQUATION

[Sec. 2 10

practically never depends on the detection of a lone signal pulse, but on
reception, from the same range and bearing, of repeated signal pulses.
This has a profound influence on the statistical problem that we have
been discussing because, whereas the noise fluctuations during successive
sweeps 1 are completely independent, the signal can be made to appear
at the same position in each sweep. To take advantage of this essential
difference between signal and noise it is evidently necessary to resort to
some method of information storage, or integration, which would make
use of the information contained in several sweeps. It might be possible,

Fig. 2-6.— Output noise power: (o) single sweep; (£>) average of two sweeps; (c) average of

four sweeps.

for example, to average over a number of sweeps—that is, to present to
the observer a single trace whose height at any time would represent the
average of the power output which was obtained in each of the several
sweeps at that same time (measured from the transmitted pulse). Now
this is substantially what many radar indicators do; it is so nearly what
they do, in fact, that quantitative conclusions drawn from a study of
the ideal process outlined are of practical significance and are surpris¬
ingly well borne out by actual observations. Therefore, we want to
inquire more carefully into the simple averaging or integration process.

1 We use the term “sweep” to mean one entire interval between successive pulse
transmissions. Such a term unavoidably suggests a particular type of display, but a
more general and formal terminology seems too cumbersome.

Sec. 210]

THE STATISTICAL PROBLEM

Let us turn to Fig. 2'6a, which represents a single oscilloscope trace
starting at the time of the transmitted pulse or at some known time
thereafter. This is a typical single trace showing noise only, without
signal. 1 Clearly only a rather strong signal could stand out conspicuously
among these fluctuations. Now examine Fig. 2-66 in which the average
of two noise traces is plotted, each point ih one trace being averaged
with the corresponding point in the other. The fluctuations are here
less violent. We note a scarcity of excessively high peaks: this is not
surprising as it is unlikely that very high peaks, being in any case infre¬
quent events, should occur at the same place on two original traces. In
Fig. 2-6c, four sweeps with noise have been averaged, and we notice a
further reduction in the magnitude of the fluctuations. As the size of a
signal peak (which means, really, signal-plus-noise ) will not be essentially
altered by the averaging provided the signal occurs at the same place on
successive sweeps, it will be easier to detect a small signal on the trace c
than on a. More than this we cannot say without elaborate analysis of
the statistical problem. Such analysis can be carried through by well-
known methods (see Chap. 8, Vol. 24) and one can obtain, for example, the
results displayed in Table 2T below.

Table 2 1.—Probability of Noise Exceeding Signal-plus-noise

w = 10 -1

w = 10- 2

1—*
o

w = 10~ 4

w = 10“ s

5 0

8.9

10.9

12.3

13.3

14.2

3.0

6.7

8.6

9.9

10.8

11.6

1.0

4.6

6.5

7.7

8.6

9.3

-0.8

2.7

4.5

5.7

6.5

7.3

-2.5

0.8

2.5

3.7

4.5

5.2

-4.2

-1.1

0.5

1.6

2.5

3.2

-5.9

-2.9

-1.4

-0.4

0.4

1.1

The entries in Table 21 are the strength of a signal, in decibels, rela¬
tive to the average noise power P 0 . The number n, at the left, is the
number of sweeps averaged—for example, 4 in the case of Fig. 2-6c.
The quantity w at the head of each column is the probability that an
arbitrary interval along the final averaged sweep will display a larger
deflection than the interval that contains the signal. For example, if
the signal is 4.6 db above P 0 (third row, second column) and the integra¬
tion has been carried over four sweeps, there is one chance in a hundred
that a selected interval will actually exceed in power the interval con-

* This trace was constructed, as were the others in Fig. 2-6, by random sampling of
a number field prepared according to the appropriate distribution function, the sweep
having been divided into intervals for this purpose. Again we are overlooking the
difference between a discrete and a continuous random process.

THE RADAR EQUATION

[Sec. 2-10

taining the signal. If the sweep length were equivalent to, for example,
500 intervals (remember that what we call an “interval” is about 1/(B
long), one would expect to find several (roughly, five) noise peaks in the
sweep which were higher than the signal peak. In this case we should
certainly need either a stronger signal or more integration.

Now it is the trend of the numbers in Table 2T which is of interest to
us, since any real radar problem will differ in many particulars from the
ideal process to which Table 2T applies exactly. If we select any column
(w = constant) we observe that the variation of signal power with n is
something intermediate between l/n and 1 /-\/n. For large n and par¬
ticularly for w not too small, the variation is not far from 1 /\/ n. This
implies that doubling the number of sweeps integrated, other things being
equal, allows the signal power to be reduced by a factor l/\/2. This
relation has been strikingly verified by the experiments of J. L. Lawson
and others (Vol. 24) in the detection of signals on the A-scope, under
conditions where n was large. On the other hand, for small n, and
especially for very small values of w, Table 2T would require the signal
power to vary more nearly as l/n. This is not too important in practical
radar design, for so many factors are involved in the real problem that we
cannot hope for, and do not need, a very precise answer to such questions.
We shall most frequently assume, in later chapters, that the required
signal power varies as 1/V n.

It must be observed, to put the above considerations in proper per¬
spective, that the benefits of integration are not confined to the smoothing
out of thermal or purely random noise. A very important requirement,
in practice, is discrimination against isolated but powerful disturbances
such as transients from nearby electrical apparatus, or, very commonly,
pulse interference from other radar sets. Indeed, the frequency of such
disturbances, in most locations, renders academic our earlier remarks
about the likelihood of getting an abnormally high noise peak once an
hour or so. The fact that the desired signal occurs repeatedly allows
such isolated disturbances to be discarded easily, or disregarded. Strictly
it is not integration, but a sort of coincidence selection, that is most potent
against these scattered flashes of interference. Such selection is inherent
to a greater or lesser degree in nearly all radar systems and as a rule very
little selection suffices. In practice then, it is still the noise that we have
to combat, not the interference, if we want to reduce the minimum
detectable signal power. 1

* Because this is true, an essential part of any test of the condition or quality of a
radar set includes a measurement of the noise level, or a quantity proportional thereto.
The determination of minimum discernible signal power under any reproducible
conditions of observation constitutes such a measurement.

Sec. 2-11] EFFECT OF STORAGE ON RADAR PERFORMANCE

2-11. Effect of Storage on Radar Performance. —How is the integra¬
tion process, or its equivalent, actually carried out in a radar set? The
earliest and simplest radar indicator is the A-scope, the horizontal range
sweep with vertical deflection by the signal. Usually the screen of the
cathode-ray tube does not give a persistent glow but the picture decays
immediately. It is difficult to see any integrating or storage mechanism
here, and indeed there is none. The storage is accomplished in the eye
and mind of the observer and is rather astonishingly effective. 1 Just
how it is done we do not know in detail, but we may see the results in
Fig. 2-5 (page 35). Note now the significance of the three curves in that
figure which correspond to different pulse repetition frequencies with the
same total time of observation. An increase in PRF by a factor of 16,
from one curve to the one below, reduces the signal power required by
very nearly a factor of 4. It is natural to assume that, whatever the
effective number of integrations, it is proportional to the PRF, for
constant observation time, and we may regard the experiments described
by Fig. 2-5 as evidence favoring the relation

Smi. « ~ (23)

In Fig. 2-7, which has been taken from Vol. 24 of this series, an attempt
has been made to show directly the effect of integration in the A-scope.
Here the camera has been substituted for the eye, and the number of
sweeps overlapping in one picture has been varied. Signals of different
strength are present at two positions in each sweep and by referring to
the explanation accompanying the figure, the reader will be able to trace
the improvement in discrimination from one picture to the next. The
noise and signal shown, incidentally, were derived from a linear detector.

In the case of an intensity-modulated indicator with a persistent
screen, what we have called “integration” is very nearly exactly that—
namely, the repeated addition, and hence averaging, of a number of
successive sweeps. The difference is that the number of sweeps so aver¬
aged is not sharply defined, since the luminosity of the screen decays
gradually with time. However there will be some time which is charac¬
teristic of the decay, and we can say simply that if the electron beam
traces repeatedly over the same strip of the screen, the number of sweeps
averaged will be of the order of the pulse repetition frequency times this
decay time. In practice, the radar is usually scanning. That is, before
the decay time elapses, the radar beam moves off the target and the cath¬
ode-ray-tube trace moves to a new position on the screen. The number of

1 Failure to appreciate the power of the observer to integrate was responsible for
some disappointment with early electrical integrating devices, which, through no
fault of their own, did not bring the expected improvement over the simple A-scope.

THE RADAR EQUATION

[Sec. 2-11

sweeps integrated then is limited by the number of pulses striking the
target during the scan and not by the screen persistence. If, however,
the latter is so long that storage is effective from one scan to the next, we

Fig. 2-7.—In this series of photographs, the number of A-scope sweeps recorded during
each exposure was varied from 12 to 400. Artificial signals were injected at the locations
marked, with the following strength, relative to average noise power: Si, +10 db; Si, +5db;
S,, 0 db; S t , -5 db.

must include more than one scan in estimating the amount of the integra¬
tion, and the screen persistence again enters.

Let us try to elucidate this rather complicated state of affairs by

Sec. 2-11] EFFECT OF STORAGE ON RADAR PERFORMANCE

tracing through an example of the familiar plan-position indicator, PPI.
Suppose that the effective storage time of the screen is 4 sec, and that the
angular width of the radar beam is 6°: let the rate of rotation be variable.
Assume a constant pulse repetition frequency of 500 pps. Let us begin
with the antenna stationary, pointing at a single target. The number
of sweeps available for integration, will be limited by the screen per¬
sistence and will be 4 sec X 500 sec -1 , or 2000. This will remain true,
even though the antenna rotates, until the rate of rotation becomes so
great that the beam dwells on the target less than 4 sec, in other words,
up to x rpm. With increasing speed of rotation, the number of sweeps
integrated will decrease as l/(rpm) until the beam rotates faster than
one revolution in 4 sec, at which time we begin to include more than one
scan in the integration. Then n t will begin to level off, its asymptotic
value, for high speed, being given by

(screen storage time) X (PRF) X

(beam width)

or, in this case, = 33 at speeds much greater than 15 rpm. Altogether
Hi has changed by a factor of <fo between low and high speed, or by just
the ratio of the beamwidth to 360°. 1Q _^__

If now we assume that the signal o _

power required for detection, S mic , || > m

is proportional to l/-\Ah, a plot of <SL„ f £_ /

against scanning speed will look like 1 ( s' n
Fig. 2-8. To be sure, we have so dras- n c = 2 ooo/

tically oversimplified the problems u ‘

that no significance can be claimed for o.i i io 100

the exact shape of the curve. Never- Speed Qf rotatlon m rpm

theless, the main features of the curve— lu? eC « ° f s . cann '" g speed

’ on storage gain, assuming o beam-

especially the existence of the plateau width, and 4-sec storage time, with

regions I and III, whose vertical sepa- PHF ~ 500 pps '
ration is determined by the ratio of the beamwidth to the total scan
angle—are worthy of attention, and have been confirmed by controlled
tests (Vol. 24, Sec. 9T).

The effect of scan speed on threshold-signal level is often called
“scanning loss," the condition of scan-speed zero being implied as the
standard of reference. This condition merits no more than any other
the distinction of being a standard. On the contrary, the factors
determining Sai 0 are in this case especially elusive, if one wants to take
them all into account. We prefer not to use the term “scanning loss,”
and if a basic standard of reference is deemed desirable we would choose,
on logical grounds, the single A-scope trace, which contains all the infor¬
mation normally available from a single pulse transmission. With

Speed of rotation in rpm

Fig. 2-8.—Effect of scanning speed
on storage gain, assuming 6° beam-
width, and 4-sec storage time, with
PRF = 500 pps.

THE RADAR EQUATION

[Sec. 2-11

respect to this standard all other modes of indication provide varying
amounts of storage gain, by making use, more or less imperfectly to be
sure, of information gathered on repeated pulse transmissions. Thus we
say that Fig. 2-8 describes the effect of scanning on storage gain.

The number of other independent variables, yet unmentioned, which
affect the amount of gain realized through storage is appallingly large.
The more prominent of these must be discussed briefly, if only to suggest
the scope of the general problem treated comprehensively in Vol. 24.

The video bandwidth b, as distinguished from the i-f bandwidth ®, has
hitherto been assumed to be so great as to allow reproduction of the
detected i-f signal without distortion. This is seldom true in practice
and the question arises, how does the video bandwidth influence the
signal discernibility, and how narrow can it be without harm? Making
the video bandwidth b considerably less than 1/r amounts to putting the
rectified signals and noise through a long-time-constant filter. This is a
sort of averaging, or integration process, in effect, the final output at any
instant being an average over several adjacent intervals, each of the order
of r in duration. It is clearly an integration process operating at a loss
rather than at a gain, in contrast to the sweep-to-sweep integration
discussed earlier, for it includes with the signal an unnecessarily large
amount of noise. The result is an increase in signal power required for
detection: for b « 1/r, <S mm is roughly proportional to 1/ y/b. Of Course
such a decrease in video bandwidth is accompanied by a marked deterio¬
ration in the time discrimination, or resolution in range, of the system
unless the range resolution is already limited by other factors. Because
of this, and for other reasons as well, designers have usually aimed at
adequately wide video bands.

Actually, the effect of video bandwidth narrowing would not deserve
even this much discussion here, were it not that, in a less obvious way,
a very similar effect arises from certain other influences, having to do
with the spot size and the sweep speed. Let us consider an intensity-
modulated indicator tube, such as the PPI. Let d be the diameter of
the light spot due to the beam, and let v be the speed with which the
beam is swept across the face of the tube. If d/v < r, the pulse duration,
the intervals of which we spoke earlier are spread apart on the tube; if
d/v > r, the spot overlaps several such intervals, or better, several such
intervals contribute to the same spot of light on the tube. Now this is
precisely what happened when the video bandwidth was made too narrow,
and we must expect the same consequences. In effect, the intensity-
modulated cathode-ray tube is a low-pass filter, whose bandwidth is of
the order v/d. For example, a radial sweep covering 50 miles of range
on a 7-in. PPI tube would be written in with a velocity of about 1.5 X 10 4
cm/sec. If d is 0.1 cm, the bandwidth of the system is about 150 kc/sec.

Sec. 2-11] EFFECT OF STORAGE ON RADAR PERFORMANCE

To use such a display for a 1-psec pulse would entail a penalty of about
2 db in Satin-

An extreme, indeed a limiting, case of the spot-size sweep-speed effect
is met in the type C indicator (Sec. 6-6) which presents only elevation
and azimuth data, not range. Here the sweep speed v is zero or very
nearly zero, the spot moving only as the antenna scans. All the noise
and the signal, if any, from one range sweep are piled up on one spot.
If T is the duration of such a sweep, 1 we should expect an increase in
due to this superposition of noise, of the order of \/ T/t.

Video mixing , which is practiced in certain radar applications, consists
in superimposing two radar pictures on the same screen. Because this
results in adding noise from one picture onto a signal from the other, we
would expect, and we find, an increase in S m ] n . If two similar but inde¬
pendent 2 radar pictures are superimposed on one cathode-ray-tube screen,
a signal on one of these pictures will have to be about 1.5 db, or \/2
stronger to be detected than would have been necessary if the other
picture were absent. A related problem is this: Suppose that on a single
radar indicator we simply remove the signal from alternate sweeps (by
holding off the transmitter pulse, for example). The resulting increase
in Stmn will amount to about 3 db in this case, for what we have done is
equivalent to the following two changes; (1) reduction in PRF by factor
of j with corresponding reduction in re,; (2) mixing in an equal number of
foreign noise-bearing sweeps, as in the previous example.

Whether the detector is a square-law detector, a linear detector, or
something else, will no doubt influence in any given case. 3 However,
we may as well lump together the effect of the detector, the cathode-ray-
tube modulation characteristics, the screen characteristics, and those of
the eye, and admit that no brief discussion of these factors is possible.
In most cases one has to rely on experience; that is to say, one has to
design by making relatively short extrapolations from previous practice,
or by making preliminary tests under conditions approximating those
selected.

1 Because the C-scope was found useful only for targets at short range, it was the
practice to apply a range gate covering only the useful range interval and suppressing
the electron beam during the remainder of the period between pulses. In this case
the time T represents the duration of the “on” part of the sweep.

2 By “independent,” it is meant that the signal from a radar target will appear on
one of the pictures only, or at any rate, not at the same position on each. The super¬
position is usually accomplished by interlacing the sweeps.

3 In so far as the question of discernibility can be stated in terms of the probability
of signal-plus-noise being larger than noise, the law of the detector, and indeed of any
subsequent elements, can be eliminated from the theoretical problem. Table 2T, for
example, holds for any detector whose output is a function of the absolute value of the
i-f voltage.

THE RADAR EQUATION

[Sec. 211

Although we have not arrived at a universal prescription for the
minimum detectable signal power, we have studied the influence of
various factors on S mm , and we are now in a position to predict the relative
change in <S min which will accompany some proposed alteration in the
radar system. One way to establish some absolute basis is to give the
observed value of the ratio of minimum detectable signal power to
average noise power, for one particular system. This is done in Table
2 2, in which are displayed the relevant constants of the system selected.

Table 2-2.—Characteristics of a Sample System

Type of indication. PPI; P7 screen; decay time about 7 sec

I-f bandwidth. ® = 1.2 Me/sec

Video bandwidth. 6 = 5 Me/sec

Pulse duration. r = 1.0 gsec

Pulse repetition frequency. 320 pps

Scan rate. 6 rpm

Beamwidth. 6 = 6°

Hence about 50 pulses on one point
target per scan, with negligible scan-
to-scan storage.

Sweep speed. i=2X 10 1 cm/sec 1 Note that d/v > t, which is

Spot diameter. d = 0.1 cm > not the best condition, but

J is a typical one.

Conditions of observation.Signal occurs on one scan, at known azimuth, in

one of six range positions. Observer must locate
it with 90% certainty. This corresponds to a
value of w, in Table 2-1, of the order of 10" ! .

Ratio of minimum detectable sig¬
nal power to average noise
power, under above conditions .. 1.25 (+1 db)

Working from Table 2-2, we can infer that if the system there described
had an over-all noise figure N of, for example, 15, the signal power required
at the terminals of the antenna would be = 1.25NkT(S> = (1.25) (15)
(1.37 X 10 -23 ) (291) (1.2 X 10 6 ) = 9 X 10 -14 watts. Now if for some
other system N is given, together with the new values of the parameters
listed in Table 2-2, the reader should be able to estimate S mm for that
system. The estimate will be better, of course, the less extreme the
departure from the conditions of Table 2-2. We must emphasize, how¬
ever, the limited utility of a value of iSmin obtained in this way. The
experiments upon which Table 2-2 is based were performed in the labora¬
tory under ideal conditions of observation; moreover, the value of w (the
parameter of Table 2T) is here certainly much too large for any radar
search operation, although it might not be inappropriate for the continuous
tracking of a target already detected.

The experimental determination of the maximum range of an actual
radar set is as uncertain a matter as is the calculation of the maximum
range by the method outlined in this chapter. Some arbitrary procedure
for observation must be specified, and the limit of range must be defined

Sec. 212] PROPAGATION OVER .1 REFLECTING SERFAGE

in a manner consistent with the inherently statistical nature of the
problem. That is not rendered so uncertain by these statistical

effects as to lose any usefulness is largely due to the inverse-fourth-power
law expressed by the radar equation, which makes the range relatively
insensitive to moderate changes in the system parameters.

It should not be forgotten that in these latter pages we have been
wholly concerned with that obscure marginal region between strong
signals and utterly undetectable signals. This margin is not, after all,
very broad. A glance at Table 2T, for instance, shows how very rapidly
w diminishes as the signal becomes strong. Most of the useful signals in
any radar set are strong enough to be practically unmistakable.

MICROWAVE PROPAGATION

In the first part of this chapter the radar equation was derived under
the assumption of free-space propagation. The assumption is frequently
not justified, and we must now turn to some of the important cases that
fail to fulfill one or more of the requirements laid down in Sec. 2T. We
shall try, where possible, to modify the radar equation to suit the new
circumstances, but it will be our broader purpose to describe, if only
qualitatively, certain propagation phenomena peculiar to the microwave
region. This is a vast subject. It includes some exceedingly difficult
problems in mathematical physics, not yet completely solved; it includes
topics in meteorology; above all, since it involves the weather and the
variegated features of landscape and seascape never susceptible of exact
mathematical description, it includes a large collection of observations
and experience, rarely easy to interpret. We could not here treat such
a subject, comprehensively, but certain aspects with which the radar
engineer should be familiar are not hard to explain. Their influence on
radar planning and design is felt, or should be, at a very early stage.

2-12. Propagation over a Reflecting Surface. —If the transmission
path lies near a reflecting surface it may be possible for energy to reach
the target, and hence also for scattered energy to return to the radar
antenna, by way of the surface as well as directly. The result of combin¬
ing the direct and the reflected wave at the target will depend on the
relative intensity and phase of the reflected wave, which in turn will
depend not only on the difference in the length of the two paths but upon
changes of phase or intensity introduced in the process of reflection.
The analysis is very easy in the case of a flat, perfectly reflecting, surface.

Let us consider a nondirective transmitting antenna A located at a
height hi above a flat reflecting surface S, as in Fig. 2-9. The field
strength at some other point B of height h 2 can be described by giving
the ratio of the field strength at that point to the field strength which
would have been observed in the absence of the reflecting surface—in

THE RADAR EQUATION

[Sec. 212

other words, under free-space conditions. It is this ratio, which we shall
call F, that we want now to compute.

The difference in length between the paths AB and AMB, if the angle
9 is small, is given quite closely by

___ _ = 2 hM

This is responsible for a difference in electrical phase of Airh^/RX radians
between the two waves arriving at B, to which we must add any phase

*>1 ~~8~- _- \ - S

h 2

/y /////////\t)) ) )^l U^HT) TT71~fyTTTT7TT7TT7T7H~rTTTTT77~rnTT.

- R -

Fig. 2-9.—Propagation over a flat reflecting surface.

shift \p resulting from the reflection of the one wave at M. The total
phase difference <j> is then

. I i Aichjiz /oe\

<#> = V H-' (25)

If the reflection at M is total, both waves arriving at B will have sub¬
stantially the same intensity, namely, that corresponding to free-space
propagation. 1 Taking the phase difference into account, then

F- = 2(1 + cos 4>). (26)

The angle contained in <j>, depends upon the nature of the reflecting
medium, upon the angle 6 between the surface and the direction of wave
travel, and upon the polarization. If the surface were a perfect conduc¬
tor, would be 7r radians for horizontal polarization (electric vector
parallel to surface) and zero for vertical polarization 2 (magnetic vector
parallel to surface). We shall be chiefly concerned, however, with the
surface of the sea, and to a lesser extent with land, and these mediums
behave more like dielectrics than conductors at microwave frequencies.
For horizontal polarization it is still true that \p = *■, but for vertical
polarization the situation is more complicated. If 6 is considerably

1 The fact that the waves arrive at B from slightly different directions, as well as
the effect of the slightly unequal path lengths upon the relative intensity, need not be
taken into account so long as R » hi » X.

2 This use of the terms “horizontal” and “vertical” polarization, though not
meticulous, is common radar practice, and causes no confusion when the directions of
propagation make small angles with the horizontal. Of course the electric vector
of a vertically polarized wave traveling from A to M is not precisely vertical.

Sec. 212] PROPAGATION OVER A REFLECTING SURFACE

smaller than 6°, in the case of water the phase shift \p is nearly v, for
nearly normal incidence, on the other hand, is nearly zero. Also, the
magnitude of the reflection coefficient, contrary to what we assumed in
writing Eq. (26), varies widely as 0 is changed, being in fact very nearly
zero for 0 = 6° (Brewster’s angle). This is as far as we care to pursue
this complicated matter, apart from displaying, in Fig. 2T0, curves
showing the dependence upon 0 of the reflection coefficient and the phase
shift, for reflection of 10-cm radiation at a water surface (there is very
little difference between salt and fresh water at microwave frequencies).

Angle with horizontal

Fig. 210. —Reflection by water at 3000 Mc/sec. Curve a: amplitude of reflection coef¬
ficient, vertical polarization; Curve b: phase shift at reflection, vertical polarization; Curve
c: amplitude of reflection coefficient, horizontal polarization. Phase shift for horizontal
polarization is 180° throughout range shown.

Fortunately, the case which is of the greatest practical importance,
that of nearly grazing incidence, is peculiarly easy to discuss, for if 0 is
less than, for example, 2° there is not much error in taking the phase shift
to be it and the reflection coefficient, unity, for both polarizations. In
this region, then, we can write

F 2 = 2 + 2 cos + t) = 4 sin 2 (-^j- (27)

Now F 2 measures directly the ratio of the power incident on a target at B
to that which would strike the target under free-space conditions. This
ratio, according to Eq. (27), varies between 0 and 4, the latter value being
attained when the direct and reflected waves arrive precisely in phase, or
when the geometry is such as to satisfy the condition

^ = n, an odd integer.

(28;

THE RADAR EQUATION

[Sec. 212

The effect of the interference described by Eq. (28) is to break up the
original radiation pattern of the source at A into a lobe structure, as
sketched in Fig. 2T1; at least this is an appropriate description of the
effect at a considerable distance from the source. The lowest maximum
in Fig. 2T1 occurs at an elevation angle of X/4Ai radians. Below this
angle the field strength diminishes until, at the reflecting surface itself,
it vanishes. Xo modification of the above argument is required for a
directive antenna at A, unless the directivity is high enough to affect the
relative intensity of the waves traveling along AB and AM (Fig. 2-9)

respectively. In any case, the width
of an interference lobe will be less
than the width of the primary radi¬
ation pattern since 4 h\ will certainly
be greater than the vertical aperture
of the antenna.

As the geometry of the problem
is not altered if we interchange
transmitter and target, the interfer¬
ence must affect the return of the
radar echo in the same degree as it affects the pulse transmission. There¬
fore the required modification of the radar equation is obtained by multi¬
plying by F 4 the expression given in Eq. (3) for the received signal power
S; that is,

5 = P Wf- 16sin l XT i) ™

To discuss the practical consequences of this we first distinguish
between the problems of “high coverage’’ and “low coverage.” In
the former case we are concerned with targets so high or so close that
2-rhihi/\R > 1; that is, with targets lying well up in, or above, the
lowest lobe of Fig. 2T1. Evidently the detection of such a target will
depend critically on its range and altitude. If an airplane flies in toward
the radar at constant altitude h 2 we must expect the signal to vanish
and reappear repeatedly, as the lobe structure is traversed. The smaller
X and the larger hi, the more finely divided is the lobe pattern. A
welcome change, on the other hand, is the additional factor of 16, effective
in Eq. (29) for directions of maximum constructive interference. This
factor should double the maximum range of detection, compared to free-
space conditions. Something like this increase is actually observed,
although it should not in every case be taken for granted, in view of the
idealized model upon which it is based.

“Low coverage” refers to a situation in which the target lies w'ell
below the lowest maximum in Fig. 211, in the region where

Fig. 211.—Lobes caused by interference
of direct and reflected waves.

Sec. 2-12] PROPAGATION OVER A REFLECTING SURFACE

'Zirhihi

(30)

For this case the sine in Eq. (29) can be replaced by its argument, leading
to

S = 4 ttP

G l o{hJnY

X-R*

(31)

We see that in this region the signal strength falls off as 1 /R s rather than
\/R i , if the other factors are held constant. This region is often referred
to loosely as the “eighth-power region,” or occasionally as the “far zone.”

Fig. 212.—Radar performance over water. Target : 5000-ton freighter. Antenna height:

21 ft.

As radar and target are separated, keeping hi and hi constant, the range
at which this inverse eighth-power dependence begins varies as the
reciprocal of the wavelength; in other words, the longer the wavelength,
the higher the lowest lobe in Fig. 2T1 is tilted, and the sooner an out¬
going target recedes underneath it. This gives a heavy advantage to
shorter wavelengths where the primary task of the radar set is to search
the sea for low-lying targets, the radar antenna itself not being mounted
at a great height. The advantage of the shorter wavelength is main¬
tained throughout the inverse eighth-power region. Comparison of Eq.
(3) with Eq. (31) shows that if two radar sets, operating at wavelengths
X, and X 2 , receive equal signals from a target in the free-space region, the
ratio of respective signal strengths in the region to which Eq. (31) applies
will be Si/S 2 = (X 2 /XO 4 .

Figure 2T2 records some radar observations made at two wavelengths
with the same ship as the target. The signal strength in decibels is
plotted against the logarithm of the range. Clearly distinguishable are
two regions in which the slope corresponds respectively to an hF -4 and to
an R~ a dependence, and the relative advantage of the shorter wavelength
in the latter region is apparent.

THE RADAR EQUATION

[Sec. 2-12

The maxima and minima which one might have expected in the
nearer region are not conspicuous in Fig. 2-12. The reason for this is
that the target was not a point with a unique height /i 2 but a complicated
object extending from the surface up to some maximum height. In this
“near zone” some parts of the ship lie on maxima and some lie in the
nulls, and the net result at any instant is some sort of average, in
the fluctuations of which one could hardly expect to discern traces of the
regular interference pattern predicted by Eq. (29). The absence of a
sharply defined break in the curve between the two regions is readily
justified on the same grounds. The location of the break, ill-defined as
it is, can however be used to compute some “effective height” fi 2 -

Although the relation in Eq. (30) fixes roughly the inner boundary of
the “R~ a region,” were we to cling to our flat-earth hypothesis there
would be no outer limit. Actually, of course, the region is ultimately

Fig. 2-13.—Reflection from an irregular surface.

bounded by the radar horizon, where a new and even more drastic falling-
off in signal strength sets in. In many instances, especially at microwave
frequencies, this limit occurs so soon after the beginning of the eighth-
power region as to reduce the latter to rather inconsequential size.

Before we discuss the effect of the earth’s curvature, we should
comment on certain other, less important, shortcomings of the preceding
simplified argument. For one thing, we have ignored the fact that the
reflecting suface is not smooth; even in the case of the sea, the irregulari¬
ties (waves) are both wide and deep compared to a microwavelength; in
the case of a land surface, we may be confronted with any imaginable
irregularity. Nevertheless, at least for reflection on the sea at nearly
grazing incidence, the observed reflection coefficient is rather close to
what a glassily smooth sea would give. 1 This is, perhaps, no more
surprising than the fact that an ordinary piece of paper displays, at
nearly grazing incidence, specular reflection of light, and it can be made
plausible by some argument such as this: In Fig. 2T3, two parallel rays,
AB and DE, strike a “rough” surface, the roughness consisting of a
single bump of height h. The reader will find with little trouble that the
net path difference between the two rays EF — AB is just 2 h sin ft. If

1 The reflection coefficient would have to be substantially less than 1 to change the
result significantly, so far as the radar problem is concerned.

Sec. 2-13]

THE ROUND EARTH

only this difference is small compared with X, the surface should reflect
as though it were optically smooth. But hd < X implies h < X/0, and if
6 is small, bumps which are actually large compared to X can be tolerated.

Something like this may occur in some circumstances over land.
Indeed, reflection has been observed on unusually flat terrain, such as an
airfield, at microwave frequencies. Except in such unusual circumstances
there is very little evidence of ground reflection at wavelengths of 10 cm
or less. For microwaves, then, the results of this section are almost
wholly restricted to transmission over water at nearly grazing incidence.

2-13. The Round Earth.—The distance Rh to the optical horizon,
from an observer situated h feet above the surface of a spherical earth
of diameter Do ft would be given by the formula, Rh = x/ D 0 ■ h if the
atmosphere did not bend the rays of light. Actually, the earth’s atmos¬
phere decreases in density with height, introducing a downward curvature
in all rays, which allows a ray to reach somewhat beyond the distance
given by the above formula. For rays of small inclination to the hori¬
zontal, and for heights small compared to the thickness of the atmosphere,
this effect can be taken into account by replacing the true diameter of
the earth by a somewhat larger number D. lt . How much larger it is
depends on the rate of change with height of the index of refraction of the
atmosphere. This effect may be expected to show local variations. A
reasonable choice of a “ standard ” condition leads to a value Rm = 1.33i?o,
and thence, thanks to a fortuitous numerical relation between units, to
an easily remembered formula for the distance to the radar horizon,

Rh (statute miles) = x/2fi (feet). (32)

The formula Eq. (32) predicts a somewhat greater horizon distance
than does the corresponding formula for the optical horizon, because the
conditions assumed as “standard” include a moderate gradient of water-
vapor concentration. Water vapor, although it has but a minor influence
on the atmospheric refraction of visible light, displays a very pronounced
refractive effect at all radio frequencies, including microwave frequencies.
This effect, caused by the permanent electric moment of the water
molecule, can, in some circumstances, drastically affect the propagation
of microwaves in a manner to be described in the next section.

Confining our attention for the moment to the atmosphere of “stand¬
ard” refractive properties, to which Eq. (32) applies, let us see why it
makes sense to speak of a microwave horizon when radiation of much
lower frequency, as is well known, travels far beyond any such horizon.
In the first place, the ionosphere does not, to any appreciable degree,
reflect or refract microwaves. In the second place, the spreading of
waves around the curved surface of the earth, essentially by diffraction,
is much reduced at microwave frequencies because the wavelength is so

THE RADAR EQUATION

[Sec. 213

small compared with the size of the obstacle, to put it very crudely.
There is some spreading of this sort, of course, and it is a phenomenon
upon which a good deal of theoretical effort has been expended. Methods
have been developed for calculating the intensity of the radiation in the
“diffraction region,” that is, beyond the horizon (Vol. 13, Chap. 2). In
this region, however, the field strength normally diminishes so rapidly
with increasing range that any additional radar coverage thus obtained
is of little value. From the point of view of the radar designer, targets
over the horizon might as well be regarded as totally inaccessible under
“standard” conditions of propagation.

Distance in miles

Fig. 2-14. —Coverage diagram for 2600 Mc/sec, transmitter height 120 ft. Solid curve for
totally reflecting earth. Dotted curve for nonreflecting earth.

As for regions well within the horizon, the curvature of the earth at
most complicates the geometry of the interference problem discussed in the
preceding section. Naturally, we have no right to apply Eq. (29), as it
stands, to targets near the horizon. We need not concern ourselves here
with these complications, which are adequately treated in Vol. 13.
Methods have been worked out for rapidly calculating the field strength
over a curved reflecting earth. The radar designer usually prefers to
display the results in the form of a coverage diagram, which shows contours
of constant field strength plotted in coordinates contrived to show directly
the effect of the curvature of the earth. One such contour, shown in
Fig. 2T4, is calculated for an omnidirectional antenna transmitting at
2600 Mc/sec from a height of 120 ft above a totally reflecting earth.
The dotted curve is the corresponding contour with a nonreflecting earth.
Both contours would usually be modified by the directional pattern of the

Sec. 2-14]

SUPERREFRACTION

radar antenna and it is not difficult to take this into account in the
calculation. Note the exaggeration of the vertical scale.

A contour of constant field strength is a contour of constant power
intensity as well; moreover, the intensity of the signal received from a
radar target of given cross section, located anywhere along such a contour,
is the same. 1 Thus, if the proper contour is chosen it will represent, as
nearly as any curve can, the boundary of the region in which a given
target can be detected. The reader’s earlier introduction to some of the
statistical factors involved in radar should prepare him for the warning
that such coverage diagrams are not to be taken too literally. They are,
nevertheless, useful in the planning and design of long-range search radar.

2T4. Superrefraction. —As we have seen, the effect of the normal
vertical gradient of refractive index in the atmosphere is to introduce a
slight downward curvature in the path of light and of microwaves. Were
this curvature only a few times greater, it would equal the curvature of the
earth itself, and it would be possible for a ray to bend around the earth
without leaving the surface; in other words, there would be no horizon.
Whatever misgivings we may have about the use of the word “ray” in
this connection, it would not be surprising if some interesting departure
from standard microwave propagation were to manifest itself under such
conditions.

Refractive index gradients of the requisite strength (5 parts in 10 s per
ft) can be produced under some conditions by temperature gradients
alone. For example, if land heated by the sun cools by radiation at
night, a fairly thin layer of cold (therefore dense) air may be formed just
above the ground, which results in an unusually rapid decrease of refrac¬
tive index with height, the index of the lowest layer being abnormally
great.

A more widespread cause of strong vertical gradients in refractive
index, and therefore of excessive bending of rays, is the refractive effect
of water vapor mentioned earlier. Over most of the surface of the ocean
the region above the water is not saturated with water vapor, whereas
the layer directly in contact with the water must be very nearly saturated.
There is, in other words, a continual evaporation of water from the sea

1 One must be careful not to confuse the directional pattern of an antenna with
the plot of contours of constant intensity in the field of the antenna, which it occa¬
sionally superficially resembles. If we plot the gain of an antenna as a function of
angle , in polar coordinates, we have an antenna pattern that has meaning, strictly,
only if the antenna is isolated in space. On the other hand, contours of constant
intensity, the coordinates of which refer directly to positions in space, can be used to
describe the radiation field no matter what the surroundings or type of propagation
involved. The fact that a signal of the same intensity is received from a target at
any position on one such contour does not depend on the inverse-square law or any
other law of propagation but only on the Reciprocity Theorem.

THE RADAR EQUATION

[Sec. 2-14

and a diffusion of the vapor upward into the overlying air mass. This
implies the existence of a vertical gradient in the concentration of water
vapor with, normally, the highest concentration at the surface and
decreasing upward.

A typical condition to which such an effect may lead is that of a
relatively shallow layer just above the surface within which the vertical
gradient of refractive index is negative and exceeds the critical value of
5 parts in 10 s per ft. Such a region is called a “duct” for reasons that
will appear shortly, and the level at which the gradient has just the critical
value is called the “top of the duct.” Were we to trace the path of an
initially horizontal ray at this level, we would find it curving downward
just enough to keep up with the curvature of the earth, and therefore
maintaining constant height. Farther down in the duct, where the
gradient is stronger, it would be possible for a ray launched at a slight
upward inclination to be bent back to the surface again and thus to
proceed by a series of bounces, trapped as it were, within the duct.

From this temptingly graphic picture of propagation within a duct
it is easy to draw false conclusions. Since the description of the process
in terms of rays, traced by the rules of geometrical optics, nowhere
involves the wavelength of the radiation, we should be led to expect
similar effects at all frequencies for which the index of refraction has the
same value, namely for all radio frequencies. But, actually, ducts such
as we have described have no observable effect on the propagation of low-
frequency radio waves. The reason for this is that the duct is effective
in “trapping” and guiding radiation only if the wavelength is less than
some critical value determined by the height of the duct and the steep¬
ness of the gradient of refractive index within the duct. The ducts
which we have described have no great vertical extent, their heights
being of the order of a few tens, or at the most a few hundreds, of feet;
their influence on propagation is usually confined to frequencies in the
1000-Mc/sec range and above. 1 For gradients in refractive index which
would not be unusual in these surface ducts over water, the relation
between height of duct and the longest wavelength strongly affected by
the duct is suggested by the figures in Table 2-3.

Table 2-3

Height to top of duct, ft.

.. . 25

100

200

400

Longest wavelength trapped, cm*.

... 1.8

* These numbers are based on an arbitrary, although reasonable, criterion for trapping, and upon a
simplified model in which the refractive index decreases upward through the duct at the constant rate
of 8 parts in 10® per foot. They are intended only to be illustrative.

1 In certain parts of the world, the effect of trapping has been observed for fre¬
quencies as low as 200 Mc/sec.

Sec. 214]

SUPERREFRACTION

That the height of the duct and the wavelength should be related,
and in such a manner that the heights involved are hundreds of times
greater than the corresponding wavelengths, may perhaps be made
plausible to the reader acquainted with propagation through waveguides.
The duct is, in a sense, a waveguide. Let us consider an oversimplified
model of a duct in which the index of refraction, n i, is constant from the
surface up to some height a, where it abruptly changes to n 2 (Fig. 2-15).
If n i exceeds n 2 by some very small amount 5, both ni and n 2 being very
nearly unity, a wave incident on the boundary CD at a grazing angle a
smaller than \/25 will experience total internal reflection. Under such
conditions the region between AB and CD can be regarded as the interior
of a waveguide bounded by two reflecting surfaces. But in an ordinary

Fig. 2-15.—Propagation within a duct (oversimplified).

waveguide there is a basic relation between the width of the guide and the
angle of incidence of the plane waves into which the simpler waveguide
modes can be resolved. The longer the wavelength and the narrower
the guide, the larger the angle a according to a relation which for very
wide guides reduces to a = X/2 a. But if, in our model sketched in Fig.
2-15, a becomes larger than x/25, total internal reflection no longer
occurs, and the energy leaks rapidly out of the guide. We might there¬
fore anticipate some such restriction as X/2 a < \/25 or X 2 < 8 a,'-5 for an
effective duct. The form of this result is not inconsistent with the
figures quoted above which were based on a constant gradient of ni in
the duct, although it must be admitted that we have brutally over¬
simplified a problem that abounds in mathematical difficulties and
subtleties.

Actually, no sharp distinction between trapping and standard propa¬
gation can be drawn. Even our naive model suggests this; for we need

THE RADAR EQUATION

[Sec. 2-15

not require total reflection at CD to get appreciable guiding for a con¬
siderable distance. Nor does the source of radiation have to lie within
the duct to permit a portion of the energy to be partially trapped in the
duct, although it may not be too far above it. The variation of field
strength with distance from the transmitter and height above the surface
is very complicated, and to cover this type of propagation by a mere
modification of the radar equation is entirely out of the question, as the
reader who pursues this subject into Yol. 13, where it is treated at length,
will learn. It is perhaps best here to summarize the aspects of super-
r"fraction which have a significant bearing on radar planning and design.

1. The guiding of microwaves by refractive anomalies of the duct
type appears to be the sole means by which coverage beyond the horizon
can be obtained. Extensions of range up to several times the horizon
distance have often been observed.

2. The most prevalent, the best understood, and probably the most
important example of the type is associated with the surface evaporation
duct, which seems to exist most of the time over large areas of the oceans
of the world.

3. Short wavelengths are required to take advantage of the guiding
effects of ducts, and, for surface ducts, low antenna (and target) heights.
This is especially true of the evaporation duct.

4. Substandard as well as superstandard radar ranges can be caused by
refractive anomalies, if the transmission path is nearly horizontal.

5. Propagation at angles steeper than a few degrees with respect
to the horizontal is not affected by the refractive anomalies here discussed.

2-16. Attenuation of Microwaves in the Atmosphere.—The earth’s
atmosphere, excluding the ionosphere, is for all practical purposes
transparent to radio waves of frequency lower than 1000 Mc/sec. Even
over a transmission path hundreds of miles long no appreciable fraction
of the energy in the radio wave is lost by absorption or scattering in the
atmosphere. With the extension of the useful range of radio frequencies
into the microwave region we have at last entered a part of the electro¬
magnetic spectrum to which the atmosphere is not wholly transparent.
Indeed an upper limit to frequencies useful for radar, imposed by the
properties of the atmosphere, is now within sight. The radar engineer
must therefore acquaint himself with certain phenomena falling hereto¬
fore within the exclusive province of the molecular spectroscopist.

Broadly speaking, there are two ways in which energy can be dis¬
sipated from a radar beam: (1) by direct absorption of energy in the
gases of the atmosphere; (2) through absorption or scattering of energy
by condensed matter such as water drops. All such processes lead to an
exponential decrease of intensity with distance from the source, super¬
imposed on, and eventually dominating, the inverse-square dependence.

Sec. 215]

ATTENUATION OF MICROWAVES

The effect is therefore truly an attenuation in the sense in which the word
is applied to transmission lines, and is properly measured in decibels per
kilometer. We shall discuss first the absorption by the gases of the
atmosphere.

Of the three abundant gases of the atmosphere—nitrogen, oxygen,
and water vapor—the latter two are intrinsically capable of interacting
with and absorbing energy from a radio wave by virtue of the permanent
electric dipole moment of the water molecule and the permanent mag¬
netic dipole moment of the oxygen molecule. We know, however, that
molecules absorb radiation in more or less well-defined absorption lines,
or bands, and we have to inquire whether either of these molecules
exhibits absorption lines in the microwave range—that is, at frequencies
much lower than those usually associated with molecular absorption
spectra. It has been found that both oxygen and water vapor do in fact
display such absorption. Although the effects observed would be
classed as very weak "by a spec.troscopist, radar involves transmission
over such long paths that very serious attenuation is encountered in
certain parts of the spectrum. In Fig. 2-16 are plotted curves showing
the course of the water vapor absorption and oxygen absorption, as a
function of wavelength. The absorption is measured by the rate of
attenuation in decibels per kilometer.

The most prominent feature of the water-vapor absorption is a single
“line” which appears as a broad maximum centered about 1.3-cm
wavelength, superimposed on the residual effect of a multitude of far
stronger lines located at much shorter wavelengths. The solid part of
the curve is based on extensive direct measurements. These confirmed
the main features of the theoretical predictions, 1 on the basis of which
the remainder of the curve has been sketched in; one cannot, however,
rely on the quantitative accuracy of the dotted part of the curve. The
curve is plotted for an atmosphere containing 10 g of water vapor per
cubic meter. This corresponds to a relative humidity of 66 per cent
at a temperature of 18°C, for example. Over the range of absolute
humidities normally encountered in the atmosphere one may assume
that the attenuation is simply proportional to the absolute humidity.
The rapid rise of the curve below 3 mm is evidence of the powerful
absorption displayed by water vapor throughout the far infrared. No
further transparent regions are to be found until we reach a wavelength
of the order of 15 microns (0.0015 cm).

The oxygen absorption rises to a high peak at 5-mm wavelength;
this has been quantitatively verified by direct measurement. At longer

1 J. H. Van Vleck, “Further Theoretical Investigations of the Atmospheric Absorp¬
tion of Microwaves," RL Report No. 664, March 1, 1945. See also Vol. 13 of
this series.

TIIE RADAR EQUATION

[Sec. 2-15

wavelengths, in contrast to the behavior of the water-vapor curve, a
residual absorption persists up to wavelengths of the order of 30 cm.
This effect is small enough to have escaped experimental detection,
but it is clearly predicted by the theory. 1 Except near the center of the
absorption maximum, the attenuation due to oxygen should vary about
as the square of the pressure; hence the effect rapidly diminishes at
high altitudes. It is perhaps unnecessary to remark that attenuations

Wavelength in cm

Fig. 216.—Attenuation caused by water vapor (Curve a) and oxygen (Curve b).
Curve a applies to an atmosphere containing 10 g of water vapor per m 3 . Curve b applies
to an atmosphere which is one fifth oxygen, at a total pressure of 70 cm Hg.

due to independent causes, such as water vapor and oxygen, are directly
additive.

Water drops in the atmosphere can affect the passage of microwave
radiation in two ways. In the first place liquid water is a very imperfect
dielectric at microwave frequencies, and absorbs energy from an oscillat¬
ing electric field just as any lossy dielectric would. For extremely small
drops, such as those in fog or clouds, this is the only important effect,
and in this limiting case the attenuation at a given wavelength is simply
proportional to the aggregate liquid water content of the atmosphere,

1 J H. Van Vleck, op. cit.; see also Vol. 13.

Sec. 2-151

ATTENUATION OF MICROWAVES

measured, for instance, in grams per cubic meter. 1 The effect of larger
drops is more complicated, depending not only upon the total mass of
water per unit volume, but upon the diameter of the drops as well. The
absorption process itself is no longer simple, and scattering of energy by
the drops, which depends very strongly on the ratio of wavelength to
drop diameter, begins to play a role. Energy scattered out of the
directed beam must, of course, be counted as lost.

Fig. 217.—Solid curves show attenuation in rain of intensity (a), 0.25 mm/hr (drizzle);
(b), 1 mm/hr (light rain); (c), 4 mm /hr (moderate rain); (d ), 16 mm/hr (heavy rain).
Dashed curves show attenuation in fog or cloud: ( e), 0.032 g/m 3 (visibility about 2000 ft);
(/), 0.32 g/m 3 (visibility about 400 ft); ( g), 2.3 g/m 3 (visibility about 100 ft).

The attenuation resulting from these effects can be calculated for
drops of any given diameter. Reliable and accurate though they may
be, such results are not in themselves of much use, for it is neither
customary nor convenient to describe a rain in terms of the drop diameter
and the number of drops per cubic meter. In any case, the drops are
never all of one size and it is not sufficient to know merely the average
diameter. Instead, one has to make use of empirical meteorological
data correlating drop size (really distribution-in-size) with precipitation
rate to arrive finally at a relation connecting attenuation in decibels

1 This conclusion holds so long as the diameter of the drops is very much less than
X/n, where n is the index of refraction of water at the frequency in question.

THE RADAR EQUATION

[Sec. 2-15

per kilometer, with precipitation rate in millimeters per hour. The
most extensive analysis of this sort has been carried out by J. W. and
D. Ryde, upon whose work 1 the curves of Fig. 2-17 are based. The direct
measurements of attenuation and rainfall which have been made confirm
these predictions satisfactorily. The chief difficulty in such experiments
is connected with the measurement of the rainfall, which is homogeneous
in neither time nor space.

The dashed curves of Fig. 2T7 show the attenuation in fog or clouds
which, as we have said, does not depend on the drop diameter. Accord¬
ing to Ryde a certain limit of optical visibility can be, at least loosely,
associated with each of the dashed curves. For the conditions to which
Curve / applies, for example, the optical range is limited to about 400 ft.
At a wavelength of 3 mm the radar range could be 50 to 100 times as
long.

It would be easy, but not very instructive, to introduce an exponential
factor into the radar equation to take account of the attenuation that
we have been discussing. We leave this task to the reader, who will
find no difficulty in calculating, for any given case, the reduction in range
caused by a specified strength of attenuation, which is effective, of
course, on both the outgoing and return path. One general observation
should be made, however, which is that the effect of an exponential term
in the radar equation is insignificant at very short ranges but over¬
whelming at very long ranges. What we mean by short and long is
determined by the rate of attenuation. An entirely arbitrary criterion,
which will serve as well as any other for discussion, is the range for which
the presence of the atmospheric attenuation just doubles the normal rate
of decrease of signal intensity with range. If a is the rate of attenuation
in db/km, the range R 0 so defined is given by R 0 = 8.08/a km. At
shorter ranges than this the inverse-square law is the more important
factor; at ranges greater than R 0 the exponential factor controls the
situation and any slight improvement in range must be bought at enor¬
mous price. In other words, once attenuation takes hold, it is of little
avail to struggle against it.

1 J. W. Ryde and 1) Ryde, Report 8670 of The Research Laboratory of General
Electric Company, Ltd. This is a British publication.

CHAPTER 3

PROPERTIES OF RADAR TARGETS

SIMPLE TARGETS

By A. J. F. Siegert, L. N. Ridenour, and M. H. Johnson 1

3T. Cross Section in Terms of Field Quantities. —In the preceding
chapter the quantity “cross section of a target” was introduced phe¬
nomenologically. Theoretical considerations which in certain cases
will allow the prediction of the value of these quantities from the known
properties (shape, material) of the target will be presented in this chapter.
The following considerations will be restricted to cases where the indi¬
vidual target is sufficiently small, compared with the distance from the
transmitter, to permit the incident electromagnetic field at the target to
be approximated by a plane wave propagating in the direction of the
target away from the transmitter; this is chosen as the z direction.
The problem of finding the cross section then reduces to the mathe¬
matical problem of finding that solution of Maxwell’s equations which
at large distances from the target reduces to the incident plane wave
and at the target fulfills the proper boundary conditions.

Suppose a solution of this problem has been found. At large distances
from the target the component of the electric field parallel to the receiving

dipole can be written in the form

E 0 e x + S -

-(r — ct)

+ terms

decreasing faster than r _1 , where E o is the amplitude of the incident plane
wave, S/r is the amplitude of the only important part of the scattered
wave, X the radar wavelength, c the velocity of light, and t the time.
Usually E 0 and S contain complex phase factors; S is in general a function
of the scattering angles. In the following discussion the symbol S R is
used to denote the value of S in the direction of the receiver. In terms
of E o and S R , the cross section o- defined in Sec. 2-3 is given by

( 1 )

3-2. Rayleigh Scattering from a Small Sphere. —As an illustration of
the use of this equation, we shall derive the Rayleigh law for the case

'Sections 31-3-4 and 3-6 by A. J. F, Siegert, 3-5 by L. N. Ridenour, and 3-7 bv
M. H. Johnson.

fi3

PROPERTIES OF RADAR TARGETS

[Sec. 3-3

of back scattering from a sphere of radius a small compared to the radar
wavelength. In this limiting case the incident field is considered homo¬
geneous over the extension of the target. In the homogeneous field the

— —cl

sphere becomes an electric dipole with a dipole moment pe x , where

V = a3Eo ( 2 )

and e is the dielectric constant. The field of this dipole, observed at a
distance r in the wave zone and in a direction perpendicular to the
polarization, is

The cross section is therefore

If |e] » 1, which is true, for instance, for a raindrop, we obtain the
simpler expression

V = 4 7r ° 2 ’ ( 5 )

which in this form serves to compare the radar cross section with the
“geometric cross section” 7ra 2 .

For the case of a metal sphere, one would be tempted to use the same
formula with |«| = °°. This, however, is not correct, because, in the
case of a conducting sphere, surface currents which have a magnetic
dipole moment are induced by the field. The radiation of both the
electric and the magnetic dipole must therefore be considered. We then
obtain

3-3. Scattering of a Plane Wave by a Sphere. —The general problem
of scattering of a plane wave by a sphere is solved in detail in J. A.
Stratton’s book, Electromagnetic Theory (pages 563 ff), and references to
the original papers can be found there. The cross section for back
scattering from a metal sphere 1 divided by ira 2 is plotted vs. a/\ in Fig.

1 P. J. Rubenstein, RL Report Xo. 42, Apr. 3, 1943. X'umerioal values for the
problem of scattering from a dielectric sphere can be found for certain values of the
dielectric constant in the references given by Stratton, Electromagnetic Theory,
McGraw-Hill, X T ew York, 1941, p. 563 ff. See also Robert Weinstock, RRL Report

Sec. 3-4] APPROXIMATIONS FOR LARGE METAL TARGETS

31, where a is the radius of the sphere and X the radar wavelength. For
wavelengths large compared to the radius, the cross section is given by
Rayleigh’s law. In the opposite limiting case (X « a) the cross section
approaches the geometrical cross section to 2 . Between these limits are
the resonance maxima.

flat

0.6

0.4

0.2

0.1

0.05 0.1 0.2 0.4 0.6 1.0 2 4

a/A

Fig. 31.—Back scattering from a metallic sphere-. In the region where the line is shown
dotted, no calculations have been made.

3-4. Approximations for Large Metal Targets. 1 ^— For metal targets
whose dimensions as well as radii of curvature are large compared with
the radar wavelength, the following approximation yields good results.
For every surface element the current is used which would be caused by
the incident field if the surface element were a part of an infinite plane
sheet. The radiation from all the surface elements is added in the proper
phase relations, and the resultant field is considered as the scattered field
from the target. For a flat metal sheet of area A perpendicular to the

No. 411-125, Nov. 14, 1944 (for cylinder and sphere); Morse and Rubenstein, Phys.
Rev., 64, 895 (1938) (for elliptical cylinder); L. J. Chu, RRL Report No. 4, Oct. 22,
1942; Marion C. Gray, “Reflection of Plane Waves from Spheres and Cylinders,”
BTL Report MM 42-130-95.

' 1 J. F. Carlson and S. A. Goudsmit, “Microwave Radar Reflections,” RL Report
No. 43-23, Feb. 2, 1943.

PROPERTIES OF RADAR TARGETS

(Sec. 34

incident radar beam we thus obtain the cross section

4ttA 2

(7)

For general angles of incidence the cross section is a function of the
angle of incidence and it varies very rapidly when, as is assumed here,
the wavelength is small compared with the linear dimensions of the plate.
In a diagram of return power vs. angle of observation these variations
show up as the “lobes.” The strong main lobe is normal to the plate and
the side lobes decrease rapidly with increasing angle. For small angles
6, but excluding the main lobe, the average cross section S (averaged over
several lobes) is given approximately by

47tX 2

(8)

This result is independent of the size of the target, subject of course to
the limitation that the linear dimensions of the target are large compared
to the.wavelength.

For a cylinder of radius R and length l, both large compared to X, we
obtain

P/2

<r = 2rr ~ (9)

for incidence perpendicular to the axis. For the same cylinder, if the
beam forms an angle 9 with the normal to the axis the average cross
section (averaged over several lobes) is approximated by

2 7T0 2 ’

( 10 )

valid for small angles 6 excluding the main lobe.

For curved surfaces, the formulas of geometrical optics can ordinarily
be used. 1 For a segment of spherical surface of radius R we find

a = tR- ( 11 )

independently of the size of the segment and of the wavelength X. This
formula is valid as long as the diameter d of the segment (perpendicular
to the incident beam) is larger than y/2\R, and provided that the edge of
the segment deviates sufficiently (>X/4) from a plane perpendicular to
the incident beam, since otherwise edge effects may become important.
If the surface is not spherical the formula is still valid if we take for R the
geometric mean of the two principal radii of curvature. The result is
the same whether the concave or convex side is turned toward the radar
transmitter.

1 For more detailed discussion see Vol. 13 of this series. Chap. 6.

Sec. 3-5]

THE CORNER REFLECTOR

3-6. The Corner Reflector. —It is often desirable to make a compact
radar target with a large cross section. A flat plate of dimensions large
compared to a wavelength exhibits a large cross section when viewed
along its normal, because of specular reflection, but the cross section falls
off sharply in other directions [see Eqs. (7) and (8), Sec. 3-4], The
problem of designing a target that will give strong specular reflection for
almost any direction of illumination has been solved by taking over into
microwave radar practice the corner reflector familiar in optics. The small
glass reflectors used in highway markers work on this principle.

A corner reflector consists of three mutually perpendicular intersecting
planes (Fig. 3-2a). If a beam is directed into the corner formed by the
planes, triple reflections occur which send it back in the direction from

which it came (Fig. 3-2 b). The effective area for triple reflection depends
on the direction in which the corner is viewed, but it is large over most
of the octant in which a single corner is effective. When the area for
triple reflection grows small, double reflection (from two planes whose
line of intersection is nearly normal to the line of sight) and single reflec¬
tion (from a plane nearly normal to the line of sight) begin to make
important contributions to the radar cross section. A single corner will
be effective only for directions of illumination that cover one octant of a
sphere centered at the reflector, as has been remarked; but all directions
can be covered by making a cluster of eight such corners (Fig. 3-3).

We can find the cross section for a corner by considering it equivalent
to a flat reflecting plate whose area is the effective area of the corner for
triple reflection. Equation (7) gives, for area .4 and wavelength X, the
cross section

4irA 2
a = “tf"

The maximum area for triple reflection will be that afforded by the corner
when it is viewed along its axis of symmetry. This maximum area is
that of the regular hexagon formed by cutting off the corners of the,
projection of the corner on its axis of symmetry; it is given by

PROPERTIES OF RADAR TARGETS

[Sec. 3-6

-'1 max

y/%

where a is the edge of the corner,
section

max

This yields for the maximum cross

4 TTO 4

sis’

showing that the free-space range at which a corner reflector can be seen
by a given radar is proportional to its linear dimensions. Figure 3-4
shows the maximum cross section at various radar frequencies as a
function of edge length.

As a/\ (and consequently the gain of a corner reflector) is increased,

greater attention must be paid
to the mechanical construction
of the reflector. When the angle
between one pair of planes differs
from 90°, the triply reflected re¬
turn from the corner splits into
two divergent beams, with a con-

Fig. 3-3.—A cluster of corner
reflectors.

Fig. 3-4.—Maximum scattering cross section
of triangular corner reflector.

sequent reduction in signal return. If two angles are in error, there
are four beams; if all three angles are wrong, six beams result. The
theory of the effect of errors 1 yields the result that a loss in returned
signal of 3 db is caused by a displacement of the outer edge of the corner
of about X/2. This limitation requires extremely close attention to the
mechanical construction of corner reflectors of high gain. It also presents
the possibility of applying modulation to the reflection from a corner by
slight motion of one side.

3-6. Target Shaping to Diminish Cross Section. —A corner reflector
gives a radar return by specular reflection for nearly all directions of

1 R. C. Spencer, “Optical Theory of the Corner Reflector,” RL Report No. 433,
Mar. 2, 1944.

Sec. 3-7]

USB OF ABSORBENT MATERIALS

approach. A target consisting of two planes intersecting at right angles
gives specular reflection for all directions of observation perpendicular to
the line of intersection. A cylinder standing perpendicular on a plane is
also strongly visible for most directions of approach. If the problem is,
on the contrary, to construct a target with a low radar cross section for
most directions of approach, such configurations must be avoided.
Furthermore, to eliminate ordinary specular reflection, surfaces perpen¬
dicular to the probable directions of observation must be eliminated.
Partial camouflage of targets has been achieved by proper shaping.

3-7. Use of Absorbent Materials. —The possibility of reducing the
radar cross section by the use of materials absorbent at radar frequencies
has been the subject of considerable investigation. Contributions to the
cross section can be separated roughly into two parts. The first arises
from flat or gently curved surfaces of considerable area (in square wave¬
lengths) which are normal to the line joining the target and transmitter.
Radiation returned from such surfaces may be properly classed as specular
reflection; cross sections arising therefrom will be referred to as “specular
cross sections.’’ If any dimension of the target is smaller than a wave¬
length, or if the backward radiation arises from the secondary maxima in
the diffraction pattern, the cross section will be referred to as a “diffrac¬
tion cross section.” When both types of backward scattering are present,
the specular cross section is usually much greater. In considering the use
of absorbent materials, this distinction must always be borne in mind.
The theory that follows is applicable only to specularly reflected radiation,
and therefore to the specular cross section.

Absorbers in general are of two types. In the first kind, reflections
occurring at the front surface of the absorber are canceled by destructive
interference with the wave that enters the layer and subsequently
reemerges. This type, analogous to the antireflection coatings applied
to optical lenses, will be referred to as “interference absorbers.” In the
second kind, the material of the absorber is so designed that no reflection
takes place at the front surface and the attenuation in the layer extin¬
guishes the entering wave. A continuous gradation from one kind of
absorber to the other exists.

Consider the reflection from an infinite plane sheet of material that
is characterized by a complex dielectric constant t and a complex magnetic
permeability m- The imaginary part of i arises from dielectric loss and
electrical conduction in the medium. The physical cause for the imaginary
part of n in the ultrahigh and microwave frequency range is not known.
Let the bounding plane between the medium and air be at z = 0. The
solution of Maxwell’s equations which represents a plane wave incident
on the bounding surface, a wave reflected from the surface, and a wave
transmitted into the medium is given by

PROPERTIES OF RADAR TARGETS

[Sec. 3 7

E y = -

H x = e ik ‘* +

E v = Ae ilz

h • - &

In these equations a is the amplitude reflection coefficient.

The boundary conditions that the tangential components of E and of
H be continuous at z = 0 immediately yield

2^0

2^0.

(121

(13)

(14)

It is clear that a will be 0 if e = p. Material with such a property will
serve as an absorber of the second kind, providing e has a considerable
imaginary part. If the refractive index n and the absorption index k are
introduced by the familiar relation

Eq. (14) can be rewritten

n + ik = %/«M,

n + u — m

at — — . —:-

n + IK ~t~

(15)

(16)

Let us now examine the behavior of an absorber of the first kind in
which the internal reflection occurs from a metal surface at the plane
2 = — d. It will be assumed that k- is small compared to n 2 . The
calculation of the resultant reflection can be made by summing the
emergent rays and adding this sum to the wave reflected from the plane
2 = 0. Let g = -XirdK/'h be the damping of a wave for one passage from
the front to back surface and return. Let 4> = 4irnd/X be the change in
phase for the same passage. Finally let IS be the transmission coefficient
of the front surface. When the index of refraction is high, Eq. (16) gives

a = 1

(17)

If it is remembered that the coefficient for the internal reflection at the
front surface is —a, the following table can be constructed.

Table 3 1.—Emergent Kays after Multiple Reflection

No. of passages through
the layer

o’

1
2
3

Amplitude of emergent
wave
a

per° ‘ ■ p

— a/9e 2( -»•"»' • 15
• (3

Sec. 3 7] USE OF ABSORBENT MATERIALS

The resultant amplitude of the wave is then

R = a + u — ae _ » + ‘» + — a 3 e 3l_c+ ‘* 1 +

f)2 e -g+i4, _ a _j_ g-e+i*

— a + 1 — aer° +l * ~ 1 + ae-“ +i i
_ a + e~"(cos <j> + i sin 0)

1 + ae _<, (cos 0 — i sin 0)

]

(18)

The minimum reflection clearly occurs when sin 0 = 0 and cos 0 = — 1.
Hpfipp

0 = (2p - 1 )t p = 0, 1, 2, • • • (19)

d = (2 p

Thus for cancellation the phase change must be t and the layer an odd
multiple of a quarter wavelength thick. The minimum reflection will
actually be 0 if

, 1 2 M

o = In - « —i
" an

and since

gn ^ gn

0 7T

( 20 )

This condition determines the necessary attenuation in the layer in order
that the emergent wave will produce complete cancellation. It is quali¬
tatively obvious that the attenuation for each passage must become
smaller as the reflection at the front surface becomes greater.

When Eq. (20) is satisfied the power reflection coefficient is given by
the relation

4a 2 cos 2 Tj

R 2 = --- ( 21 )

(a 2 — l) 2 + 4a 2 cos 2

If the bandwidth AX of the absorber be defined as the range of wavelengths
in which more than half the incident power is absorbed, it can be shown
from Eq. (21) that

^ = §£■ (22)

X ini

Therefore the bandwidth of an absorber is proportional to m and inversely
proportional to n. The qualitative nature of this behavior follows at
once from the way in w hich a depends upon n and m- For a given refrac¬
tive index, a continuous transition from absorbers of the first kind to
those of the second kind may be effected by allowing the value of m to
range from 1 to e.

Absorbent materials have been produced in Germany for the

PROPERTIES OF RADAR TARGETS

[Sec. 3-7

radar camouflage of U-boats. The type of absorber that was actually
put into service was of the interference kind. The dielectric constant
and permeability were produced by a high concentration of spheroidal
metal particles (carbonyl iron). The concentration of metal was 80 per

Angle with normal to plate in degrees

Fig. 3-5.—Effect of absorbing material on energy returned from a flat plate at various
angles of incidence. Curve a: diffraction pattern of a metal plate, electric vector of radia¬
tion normal to plane of incidence. Curve 6: plate covered with absorbing material of high
dielectric constant. Curve c: plate covered with magnetic absorbing material of low dielec¬
tric constant.

cent by weight, and values of dielectric constant and permeability were
€ = 7, m = 3.5.

An absorber of the second kind was also developed in Germany. It
consisted of a series of layers whose conductivity regularly increased with
depth. The layers were separated by a foam-type plastic whose dielectric
constant was close to 1. The absorption was excellent from 4 to 13 cm.
However, the complete absorber was a rigid structure 2} in. thick, and it
was never actually used.

Sec. 3-8]

RETURN FROM TWO ISOTROPIC TARGETS

When absorbent materials are applied to targets whose cross section
is mainly specular, the cross section is reduced by the factor jR'f-—a result
that is confirmed by field tests.

The manner in which absorbent materials influence the diffraction
cross section is shown in Fig. 3-5. The diffraction pattern of a small
plate exhibits a strong maximum at an angle corresponding to that for
specular reflection, and at other angles falls off with the oscillations shown.
If the plate is covered with absorbing material of high refractive index,
the principal diffraction maximum is greatly reduced whereas the second¬
ary maximum is in general only slightly changed. Covering the plate
with magnetic material of low refractive index not only reduces the
principal diffraction maximum, but also makes the secondary maxima
considerably lower. Generally speaking, material of high refractive
index can be expected to reduce the specular cross section while it leaves
the diffraction cross section substantially unaltered. Magnetic material
of low refractive index may, however, also effect a reduction in the
diffraction cross section.

COMPLICATED TARGETS

By A. J. F. Siegert and E. M. Purcell

Most targets are much more complicated than those dealt with in the
previous sections. A distinction will be made between “complex targets”
and “compound targets” (Sec. 3-10). The latter term denotes targets
consisting of many independent elements (rain, vegetation) which
generally fill the volume illuminated by a “pulse packet” (Sec. 4-2)
completely. The former denotes complicated targets (such as ships, air¬
craft, and structures) which are large, but still smaller than the illuminated
region. The power received from compound targets is thus dependent
on beamwidth and pulse length, since these govern the size of the pulse
packet; the signal from a complex target is not.

3-8. Return from Two Isotropic Targets. —The outstanding features
of the signal returned from complex targets—its fluctuations and its
wavelength dependence—can be studied by considering a simple model
consisting of two equal isotropic targets a distance l apart. This distance
is assumed to be smaller than cr/2, where r is the pulse duration, so that
the signals overlap—at least partly. The ratio of the received power
from the two targets to that which would be received from one of the
targets alone (at a distance large compared with l) is given by

PROPERTIES OF RADAR TARGETS

[Sec. 3-8

Fig. 3-6. —Successive
frames of a photographic
recording of an A-scope
trace at ^-sec intervals.

Because of interference, the received power varies
between 0 and 4 times the power received from
one of the targets.

A beautiful example of the change of signal
power with l, as predicted by this formula, is
given in Fig. 3-6, which shows successive frames
of a photographic recording of an A-scope trace
at xj-sec intervals. These recordings were ob¬
tained on Deer Island in Boston Harbor. The
signal on the right-hand side is received from
the antenna towers of Radio Station WBZ. The
signals received from these two towers overlap
in the center and there show the effects of de¬
structive and constructive interference. In the
last frame (No. 0311) and in the enlarged frame
(No. 0479, Fig. 3-7) the parts of the signal where
there is no overlapping are separated by a gap of
zero power due to destructive interference in the
overlapping region. In Frame No. 0303 and in
Frame No. 0538, Fig. 3-7, we have full construc¬
tive interference. The deflection of the A-scope
used was not linear in the power, so that the
highest deflection with constructive interference
is only 3 times that of the individual signals,
whereas the power itself is 4 times the power
received from the towers individually. The
change in power is due to changes in the distance
l arising from a swaying motion of the towers.
The other possible cause, change of wavelength
due to change in frequency or refractive index,
has been ruled out. 1 Correlation was actually
observed between the wind velocity and the rate
of fluctuation. The towers would have to move
only one inch relative to each other to change
from constructive to destructive interference.

In Eq. (23) we note further that the return
power from a complex target consisting of two
equal isotropic scatterers a fixed distance apart
depends upon X, and that the change in signal
for a given wavelength change increases with the
value of l. This fact has been applied in a

1 See Propagation of Short Radio Waves, Vol. 13, Sec.
6-17, Radiation Laboratory Series.

Sec. 3 9]

ACTUAL COMPLEX TARGETS

device to distinguish small targets of large radar cross section from
large complex targets such as ships by observing the change in signal
intensity caused by a change in wavelength.

3-9. Actual Complex Targets. —The actual targets encountered in
the practical use of radar are of a much higher degree of complexity than
the simple model just considered. Only a rough estimate of the cross

Fig. 3-7.—Enlarged frames of a photographic recording of an A-scope trace.

section of such targets as aircraft or ships can be obtained by calculation.
Even if one could carry through the calculation for the actual target
(usually one has to be content with considering an oversimplified model)
the comparison of calculated and observed cross section would be
extremely difficult because of the strong dependence of the cross section
on aspect. In Figs. 3-8 and 3-9 the observed return power 1 from a B-26
1 Ashby et al ., RL Reports No. 931, Apr. 8, 1946, and No. 914, Mar. 28, 1946.

76 PROPERTIES OF RADAR TARGETS [Sec. 39

and an AT-11 aircraft, respectively, is shown as a function of azimuth
angle.

The airplane in each case was mounted on a turntable in surroundings
free from other reflecting objects, and was observed with a near-by radar
set. The signal strength was automatically recorded as the airplane was
slowly revolved at a uniform rate.

35 db

In many positions, the power received changes by as much as 15 db
for a change of only in aspect angle. To a lesser, but still very notice¬
able, extent the cross section is a function of the position of the propeller,
so that modulation 1 of the received power is produced when the propeller
is rotating (Figs. 310 and 311). The modulation is far from sinusoidal,

1 Ashby, loc. cit.

Sec. 3-9]

ACTUAL COMPLEX TARGETS

and can be described better as a series of flashes. The power in the
higher harmonics decreases only slowly with increasing harmonic number.
Because of these variations of cross section, it has been necessary to
modify the definition of cross section, in order to make at least the
experimental definition unique.

40 db

In RL Report Xo. 64-10, 1 where a number of measured cross sections
are tabulated, the convention is made that the cross section attains the
tabulated value during one half of a series of time intervals. The signal
is considered as seen in a time interval A< if at least once during this
interval it was distinguishable in the noise. The interval length is

1 L. B. Linford, L>. Williams, V. Josephson, W. Woodcock, and supplement by
L. B. Linford, RL Report No. 64-10, Nov. 12, 1942.

78 PROPERTIES OF RADAR TARGETS [Sec. 3 9

m = 1.0

I'm. 3-10.—Fractional modulation of returned signal from a B-2G at blade frequency; left,
propeller rotating, right propeller stationary.

chosen as 5 sec. The cross section thus defined exceeds the average
cross section by an amount as yet unknown.

The values for cross sections in Table 3-2 have been obtained using
this definition of cross section.

Table 3-2.— Radar Cross Section of

Aircraft. Type

OS2U.'.

Curtiss-Wright 151).

J2F Grumman Amph.

H-18.

B-17...

SXB

AT-11

PBY

Taylorcraft

Aircraft
Cross Section, ft 2

. 170

. 410

. 440

.640

. 800

. 230

. 200

. 560

. 170

Sec. 3-9]

ACTUAL COMPLEX TARGETS

A more serious modification of the definition of cross section is made
necessary by the reflection of radar waves when the target is observed at
an elevation angle smaller than half the beamwidt.h and over a water
surface. In such cases, the received power is modified by the interference
of the direct wave with the reflected wave, both for the incoming and for
the outgoing wave (Sec. 2-12). The concept of cross section in the

m = l.Q

Fig. 3-11.—Fractional modulation of returned signal from a B-26, both propellers rotating.

original sense breaks down in such cases, because it is then no longer
possible to define a single quantity characterizing the target—namely the
cross section—in such a manner that the received power depends only
on the properties of the radar set (P, G, and A), on the range, and on the
cross section.

As long as the target does not extend in elevation over more than one
lobe (an assumption that is usually correct for airplanes) a modification

PROPERTIES OF RADAR TARGETS

[Sec. 3-9

of the definition of cross section can be made in a natural and simple
fashion if the target is not too near to the radar horizon. Assuming a
flat earth with reflection coefficient — 1, the power per unit area at the
target is modified by the factor

where hi and hi are the heights of the antenna and the target, respectively,
X is the radar wavelength, and R the range (see Sec. 2-12). The same
factor has to be applied again in computing the return signal to take
account of the interference along the return path. The assumption of a
flat earth is a good approximation 1 up to ranges somewhat greater than

Ahihi

The cross section is thus redefined by the equation

PG A
'4tr R 2

sin* (2,r^ 2 )

An attempt has been made in RL Report No. 401 to extend the
validity of this definition to include ship targets by determining experi¬
mentally an “effective value” for Ro- This is done by observing the
range at which the attenuation of the return signal becomes greater than
that predicted by the inverse fourth-power law. In this way the cross
sections in Table 3-3 were obtained. The procedure amounts to a replace-

Table 3-3.— Radar Cross Section of Ships

Cross section, ft 2

Type of ship

| * = 10 cm

X — 3 cm

Tanker.

.! 24 X 10 3

24 X 10 3

Cruiser.

.1 150

150

Small freighter.

.; 1.5

Medium freighter.

. 80

Large freighter.

.1 160

160

Small submarine (surfaced).

.! 0.4

ment of the real target, which extends over an elevation range from zero
to its actual height and whose illumination varies with elevation, by a
target at an “effective height” determined experimentally.

A different attempt has been made by M. Katzin, 2 who computes the

* O. J. Baltzer, V. A. Counter, W. M. Fairbank, W. O. Gordy, E. L. Hudspeth,
“Overwater Observations at .Y and .S' Frequencies,” RL Report No. 401, June 26.
1943.

s Navy Report RA3A213A.

Sec. 310 ]

COMPOUND TARGETS

effect on the received power of the variation of illumination for a vertical
rectangular sheet and uses the formula, thus obtained as a, defiwitittw v,f
cross section.

3-10. Compound Targets Extended through Space. —Targets such as
rain, vegetation, “window,” 1 or the surface of the sea are much more
complicated than the targets considered in the preceding sections. It is,
however, easier to predict and verify certain features of the return from
such targets because the compound targets here considered are composed
of large numbers of independent individual scatterers, and for that
reason statistical considerations can be used in their treatment. The
aim of this statistical treatment is to predict the probability distribution
of the returned power and of the correlation of successive measurements
of the return power.

It will be useful to distinguish between compound targets distributed
throughout a volume (rain, “window”) and those distributed over a
surface (vegetation, waves). In this section the first class is considered,
the second being deferred to Sec. 3T1.

The Rain-echo Problem .—Echoes from rain are frequently observed
on microwave radar (Fig. 3’12). Under some circumstances, the ability
to map out storm areas by radar may be put to good use. In many
applications, however, the presence on the radar screen of storm echoes
(that is, echoes from rain drops within a storm area) is objectionable for
either of two reasons. (1) A small isolated storm cloud at long range
may be mistaken for a legitimate target; airborne sea-search radar is
especially vulnerable to this kind of confusion. (2) Echoes from a storm
area may mask or confuse the echoes from targets at the same range and
azimuth.

The nuisance of “rain clutter,” which the latter effect is sometimes
called, is most severe when the radar cross section of the desired target
is small. Other factors that determine the intensity of the rain echo
relative to that of the target echo are the beamwidth, pulse length, and
wavelength of the radar, the distance to the target, and the number and
size of the water drops in the neighborhood of the target. In the case of
a radar set using a pencil beam or a simple fan beam, these factors enter
the problem as follows:

Average rain-echo intensity _ / R 2 \- ct\ Xa 0

Target-echo intensity \ .4 2 / a, ^

1 “Window” is the British and most commonly used code name for conducting
toil or sheet cut into pieces of such a size that each piece resonates as a dipole at enemy
radar frequency. When this material is dispensed from aircraft, large volumes of
space can be filled with it. It falls at a speed of only a few miles per hour. The
strong signals it returns so effectively mask the radar signals from aircraft that are
in the midst of a cloud of window that several tons of aluminum used to be dispensed

Fig. 3*12.—Echoes from a typhoon on the scope of a 10-cm shipborne radar system.

“Eye” of storm is clearly visible above center of scope.

where

R = range
X = wavelength
c ~ velocity of light
r = pulse duration
A = area of antenna aperture
N = number of drops per unit volume
cro — radar cross section of an average drop
cr t = radar cross section of target.

in this form on each European heavy bomber raid. The U.S. Army referred to this
material as “chaff”; the Germans called it “Dueppel.”

Sec. 310]

COMPOUND TARGETS

The quantity in parenthesis in Eq. (24) will be recognized as the volume
of the region, in space from which, at a, given instant, reflected signals can
be received. One must assume, to obtain Eq. (24), that the rain is
distributed over a region larger than this pulse packet and that the
target is smaller than the pulse packet.

The average total power received from all the raindrops that contri¬
bute to the return at a given range is the sum of the return powers of the
individual drops. The return powers, not the return fields, must be
added 1 because the random distribution of raindrops in space results in
random phases of the individual contributions.

The cross section <r 0 for raindrops is that of a small sphere of large
dielectric constant (Sec. 3-2) and is given by

where a is the radius of the raindrops, d their diameter, and the bar
denotes averaging over all drops that contribute to the return. Since
neither N nor the distribution in drop size is very well known, it will not
be possible to test this formula experimentally with great precision, but
the existing measurements of average intensity can be explained, assum¬
ing reasonable values of N and a 6 .

Using Eq. (25) we can now rewrite Eq. (24) as

Av erage rain-echo int e nsity _ R-crd^N ....

Target-echo intensity ° .4 XV, ’

which displays the strong dependence of rain echo upon wavelength and
drop diameter.

What has been said above pertains to the average intensity of the '
rain echo. Actually, the signal received from a given region, being the
vector sum of the waves reflected from the individual drops, fluctuates
continually in amplitude as these drops-shift in position relative to one
another. 2 This fluctuation obeys a simple statistical law, which, for our
purpose here, can be stated as follows: the probability of receiving, at

any time, an echo of intensity (power) P or greater is just e where
Pa is the average intensity over a time long compared to the fluctuation
time. Precisely the same law describes the distribution in intensity of
thermal noise power as amplified by the i-f amplifier of the radar set,
and this is one reason for the striking similarity between rain clutter and
receiver noise as seen on a radar oscilloscope. There is, however, one

1 This point is discussed in greater detail in Chap. 7, Vol. 13 of this series.

2 The changes of intensity caused by statistical fluctuations of the number of
raindrops within a pulse packet are small compared with these changes.

PROPERTIES OF RADAR TARGETS

[Sec. 3-10

essential point of difference: 1 the rate of fluctuation of the receiver output
is determined by the bandwidth of the receiver, whereas the rate of
fluctuation, in time, of the echo from a given element of volume in the
rain is fixed by the time required for the drops in the volume to assume
a new configuration. This is ordinarily so long that several successive
radar pulses find the drops disposed in nearly the same way, that is, with
changes in relative positions amounting to a small fraction of a wave¬
length only. A quantitative formulation of this statement is derived in
Yol. 24, Sec. 6-2.

The latter effect makes the detection of a desired target echo within
the rain clutter even more difficult, for the very persistence of the target
echo on successive pulses helps greatly to distinguish it from noise
(Sec. 2T0). Such help is of no avail against rain unless the target echo
is received over a time long compared to the rain fluctuation period
discussed above.

To distinguish a target in the midst of rain clutter, we must make
use of some peculiar feature of a raindrop as a radar target. One such
feature, perhaps the only one unique to rain, is that the raindrops are
round; thus the intensity and phase of the reflection from a single drop
do not depend on the direction in which the incident beam is polarized.
This cannot be said of most radar targets, which, being complicated
objects usually not rotat.ionally symmetrical about the line of sight,
show very large variations, with polarization, of the total (complex)
reflection coefficient. An experimental verification of the theory that
this property of symmetry which is peculiar to raindrops can be used
to distinguish a target signal in the midst of rain clutter has been carried
out.

Very briefly, the principle is this: if a sphere is struck by a circularly
polarized plane wave, formed by passing a linearly polarized plane wave
through a quarter-wave plate, 2 the scattered wave observed in the back-

1 There are other minor differences: the length in range of a “noise spot” is deter¬
mined by the receiver bandwidth and the cathode-rav-tube spot size. The length in
range of a “rain spot” depends on the pulse length as well. The width, in azimuth,
of a noise spot depends only on cathode-ray-tube spot size, or sweep interval, which¬
ever is larger, whereas the azimuthal width of a rain spot depends on the antenna
beamwidth.

2 Quarter-wave plates and half-wave plates for radar, entirely analogous to those
familiar in optics, can be made. What is necessary is to make the phase velocity
of the wave as it passes through the plate depend upon its direction of polarization
with respect to some direction in the face of the plate. This is done by making the
plate of a stack of parallel metal sheets spaced an appropriate distance from one
another. When a linearly polarized radar wave encounters the edges of the sheets
forming the stack, the component whose electric vector is normal to the edge passes
through unaffected. The component whose electric vector is parallel to the edge,
however, finds itself in a waveguide of great height but of finite width. Its wavelength

Sec. 311]

EXTENDED SURFACE TARGETS

ward direction will be circularly polarized. However, the sense of
rotation of the vector which represents the field of the scattered wave
is such that if the scattered wave passes back through the original
quarter-wave plate it will emerge as a wave whose polarization is per¬
pendicular to that of the initial linearly polarized wave (Fig. 3-13).

It will therefore not enter the antenna which was the source of the
original linearly polarized wave.

Experimental results are shown
in Fig. 3-14. The average intensity
of the rain echo at a given range
was reduced approximately 26 db,
while the ground targets (buildings)
which were being observed at the
same time suffered a reduction of
4 to 8 db. Imperfections of the
quarter-wave plate, as well as the
slight ellipticity of falling raindrops, prevent complete cancellation of the
rain echo.

3-11. Extended Surface Targets. 1 —In many cases the individual
scatterers in a compound target are confined to a relatively thin layer,
which can be treated as an extended surface target. Nearly all of the
signals received by airborne radar are from targets that fall into this
classification. One example is vegetation, which covers most of the
land over which an airplane is likely to fly. Another is the diffuse return
from irregularities on the surface of the sea.

Let us examine briefly the processes involved in the reception of a
radar signal from a layer of scatterers, such as the layer of vegetation
on the ground. The radar set transmits a pulse of duration r, which
travels from the airplane toward the target at the velocity c. A particu¬
lar scatterer will be illuminated for a time equal to the pulse length,
as the advancing pulse goes by, and mil send a reflected pulse of the
same duration back to the receiver. The signal received at a time t,
measured from the moment the transmitter begins to radiate its pulse,
will consist of contributions from all those scatterers which lie within
the antenna beamwidth a and within a range interval A R, where

R' — AR = ic(f - t), (27)

R r = \ct.

Fig. 3*13.—Scheme for reduction of rain
echo.

in. this guide is greater than the free-space wavelength (Sec. 11*3), and the phase of
this component can be advanced over that of the other component by any desired
amount, simply by choosing the width of the sheets along the direction of propagation
appropriately. See W. E. Kock, “Metal Plate Lenses for Microwaves,” BTL Report
MM-45-160-23.

1 By R. E. Clapp.

PROPERTIES OF RADAR TARGETS

[Sec. 3-11

As we can see from Fig. 3'15, this group of scatterers will lie within a
patch of surface of nearly rectangular shape, with its area approximately
given by

A = (Ra)(}cT sec 0). (28)

Here we have used

R = R' - i AR,

(29)

which is the range to a point in the center of the “target area,” the area
shaded in Fig. 3-15.

Rain echo

Without A/4 plate
sweep: 33 small div/mi

With A/4 plate
sweep & gain same as
above

Land targets

Without A/4 plate
sweep: 9.5 small div/mi
Rain visible only at close
range

With A/4 plate
gain increased 6 db
Broad pip at center
is artificial signal

Fig. 3-14.—A-scope observations of rain and land targets.

The radar equation was derived in Chap. 2 for the ease of a discrete
target with cross section a, Eq. (2-3b). This equation, repeated here, is

P\-G-
~ (Hr

(30)

Sec. 311]

EXTENDED SURFACE TARGETS

We can generalize this formula to the case of an extended surface target,
if we replace <s by an expression whose form will be deduced tbrougli
statistical arguments similar to those used in Sec. 3-10. As long as the
relative positions of the objects in the target layer are random, 1 we add
the power received from each object in the area to find the average

R'-AR

Fiq. 3-15.—The area contributing to the instantaneous power received from an extended
surface target is limited in range and azimuth by the resolution of the radar system.

level of the probability distribution. The average signal S will thus be
proportional to the area A, but it can also be expected to depend on
the aspect angle 6, in a way which need not be specified here beyond

1 Specifically, we require that the wave trains received from the individual scat¬
tered within the target area should combine in random phase, which will be the case
if the ranges /?, to the scattering objects are distributed with a randomness or devia¬
tion much greater than one wavelength, over a range interval A R itself much greater
than one wavelength.

PROPERTIES OF RADAR TARGETS

[Sec. 311

denoting it by a function F(&). The aspect function F(0) will thus
include three effects: (1) the amount of power intercepted by the area A
will depend upon the orientation of the surface with respect to the
incident wave; (2) only a part of the incident radiation will be reradiated
diffusely, the rest being absorbed (or, as in the case of sea return, reflected
specularly); (3) the scattered power may be reradiated preferentially
in certain directions, depending on the properties of the scatterers. If
we let F(6) include these three factors, the expression for the effective
cross section of an extended surface target becomes

a = ( Ra ) ■ (|cr sec 6) ■ F(8). (31)

Substitution of Eq. (31) into Eq. (30) will give the received signal S.

At medium and long ranges (compared to the altitude of the airplane),
the factor sec 6 is approximately unity and can be neglected. On the
other hand, for the computation of the altitude signal, 1 Eq. (31) is not
sufficiently precise, because the aspect angle 8 varies considerably over
the large area, directly below the airplane, which lies within the range
interval A R when R is approximately equal to h, the altitude. In that
case, the received signal must be obtained from an integration over the
large area contributing to the instantaneous power level in the radar
receiver. 2

GROUND-PAINTING BY AIRBORNE RADAR

By C. F. J. Overhage and K. E. Ci.aep

Airborne radar equipment has been extensively used in military
aircraft for navigation by pilotage under conditions of restricted visi¬
bility. The performance of these radar sets in displaying topographic
features below the aircraft depends on point-to-point variations in the
radar-reflection properties of the earth’s surface. The information
contained in the received echo signals is generally presented to the
observer as a brightness pattern on an intensity-modulated persistent-
screen cathode-ray tube in which radial distance from the center cor¬
responds to slant range or ground range, and azimuth to relative or true
bearing. While the coordinates of this plan-position indicator (PPI)
presentation thus lend themselves to comparison with maps, the correla¬
tion between the brightness pattern and the topographic features of
the ground is a matter of varying difficulty, depending on the nature
of the terrain, the experience and skill of the operator, and the particular

1 The first signal to arrive is the reflection from the ground directly beneath the
aircraft; it is called the “altitude signal" because its range is equal to the altitude of
the aircraft.

2 See the chapter on “The Altitude Signal,” R. E. Clapp, 'A Theoretical and
Experimental Study of Radar Ground Return.” RL Report Xo. 1024, 1940.

Sec. 3-12]

SPECULAR AND DIFFUSE REFLECTION

radar system that is used. The identification and correlation are
based upon intensity contrasts which fall into several categories, such
as the contrasts between land and water, between hill and valley, and
between built-up areas and open countryside. As each type of contrast
is discussed, it will be illustrated by radar scope photographs.

3T2. Specular and Diffuse Reflection. —Of the several ways in which
airborne radar gives its information, the most important is through the
contrast between rough and smooth surfaces. A smooth surface on
the ground appears as a black area in the radar picture, while a rough
surface appears bright in contrast. In the case of the smooth surface,
the incident radiation is deflected away, as in Fig. 3T6. Where the
ground is rough, the incident radiation is scattered in all directions, as

I'm. 3-lfl.— (a) Specular reflection. (M Diffuse reflection.

in Fig. 3T6, a part of it returning to the receiver to be amplified and
shown on the radar scope.

The signal strength from land areas is so milch greater than that
returned by water surfaces that the interpretation of land-water bound¬
aries is the simplest of all recognition problems. In a region of highly
indented coastline the presentation is so strikingly similar to ordinary
maps that navigation by pilotage can be performed even by inexperienced
operators. Situations of this type are illustrated in Figs. 3-17, 3T8,
3T9, and 3-20. In Fig. 3-17, for example, the position of the aircraft
(given by the spot at the center of the picture) can immediately be
identified by reference to the Oakland waterfront. Treasure Island, and
the Hay Bridge. Figure 3-20 illustrates the aid in recognition afforded
bv a broad river valley.

The fineness of the detail which can be shown depends on the range
and azimuth resolution of the radar system and on the sharpness of

90 PROPERTIES OF RADAR TARGETS [Sec. 312

focus (the “spot size”) of the oscilloscope. Figures 3-17 and 3-18 show
the resolution of 3-cm systems with an azimuth beamwidth of about
3°, as compared with slightly less than 1° for the 1.25-cm systems of
Figs. 3-19 and 3-20. With many radar systems the azimuth resolution
is not as fine as the range resolution, so that individual signals appear

Fig. 317.—San Francisco Bay, with Golden Gate Bridge and city of San Francisco
at left, Oakland shore at light, and Bay Bridge and Treasure Island near the center of the
picture. Wavelength =3.2 cm, altitude 8000 ft, radius 15 nautical mi. 37°51'N. 122°21'W.

as narrow circular arcs as in Fig. 3-18. In general, a radar picture may
be considered as being painted with brush strokes whose size and shape
depend on the beamwidth, pulse length, and oscilloscope spot size.
Narrow rivers and inlets can best be resolved when they are seen from the
direction which sets them parallel to these brush strokes.

Whether a particular surface appears rough or smooth depends on the
wavelength of the radar system. For example, in Fig. 3-21 the paved

Sec. 3-12]

SPECULAR AND DIFFUSE REFLECTION

airport runways stand out clearly against the grass-covered ground
between the runways. At the wavelength of 1.25 cm the grass is thor¬
oughly rough and the runways quite smooth, resulting in strong contrast.
The contrast is reduced at much shorter wavelengths (ordinary light),
for which the runways as well as the grass appears rough. At much

Fig. 3-18.—Coastal areas of Kyushu and Shikoku in the vicinity of Uwajima, Japan.
Wavelength = 3.2 cm, 3° beam, altitude 10,000 ft, radius 24 nautical mi. 33°03'N.
132°20'E.

longer wavelengths both the grass and the runways appear smooth in
comparison with wooded areas around the airport. There is still a small
signal from the grass and a smaller signal from the paved runway,
(because any irregularity scatters a certain amount of power), but on
the radar picture a surface that is flat in comparison with the wave¬
length appears dark in comparison with a rough surface, except when the
flat surface is viewed at normal incidence.

PROPERTIES OF RADAR TARGETS

[Sec. 3-13

At normal incidence the full strength of the reflected wave from a
specularly reflecting surface hits the receiver with an intensity much
larger than the signal from a diffusely reflecting surface. For this
reason the altitude signal is much stronger over water areas than over
land.

Fig. 319.—Tip of Cape Cod, Mass., with Provincetown Harbor. Wavelength = 1.25 cm,
0.8° beam, altitude 4000 ft. radius 3 nautical mi. 42°03'N. 70°06'W.

3-13. Sea Return and Ground Return. —Many surfaces are neither
perfectly smooth nor thoroughly rough. Although a quiet water surface
is as near to a specular reflector for microwaves as nature provides,
it has been observed that a water surface agitated by wind and tide
reflects a strong signal known as “sea return.” Considerable sea return
is shown in Figs. 3-17 and 3-22, but it does not interfere with identification
of the land areas. Since sea return is usually much weaker than ground
return and lacks the sharp outlines of land areas, there is little chance of

Sec. 3-13]

SEA RETURX AND GROUND RETURN

confusion between sea and land. Sea return is strongest in the direction
from which the wind is blowing. This effect is shown clearly in Fig.
3-22, which not only shows substantial sea return in the upwind and down¬
wind directions (north and south), with no visible return in directions
crosswind from the radar, but also shows a much weaker sea return in
the protected inner harbor than in the outer harbor.

Fig. 3'20.—Connecticut coast between New Haven and New London. Wavelength =
1.25 cm, 0.8° beam, altitude 7000 ft, radius 20 nautical mi. The north shore of Long
Island is faintly visible 17 mi. southeast of the aircraft. 41°23'N. 72°30'W.

For microwave radar most land areas are wholly on the rough side
of the division between rough and smooth surfaces—primarily because of
the presence of vegetation. Because the ground is thoroughly rough,
the aspect function F(d) of Sec. 3T1 takes, for ground return, the follow¬
ing simple form:

F(6) = K sin 8,

(32)

PROPERTIES OF RADAR TARGETS

[Sec. 3-13

where K is a numerical constant which can be interpreted as the reflection
coefficient of the ground. Equation (32) is based on the assumption
that every bit of the incident energy that is headed for an area on the
ground will strike some object in that area, where a fraction, (1 — K),
will be absorbed, and a fraction, K, will be reradiated, all directions of
reradiation being assumed equally probable. Some experimental

Fig. 3-21. —Airport runways at Bedford, Mass. Wavelength = 1.25 cm, 0.8° beam,
altitude 1500 ft, radius 3 nautical mi. The blank sectors to the south are shadows cast by
the wheels of the aircraft. 42°29'N. 71°19'W.

measurements have been made of the radar signals received by an air¬
borne radar system from level, vegetation-covered ground, and of the
variation with aspect angle of the intensity of the signals. These
measurements are in substantial agreement with Eq. (32).

Introduction of Eq. (32) into Eq. (31) gives the radar cross section
of the ground:

a = (Ra)(\cT sec 8)K sin 9.

(33)

Sec. 313)

SEA RETURN AND GROUND RETURN

Since the angle 9 that appears here is the angle between the plane of
the ground and the line of sight, a depends on the slope of the ground,
being larger for ground that slopes upward (as viewed from the aircraft)
and smaller for ground which slopes downward. Two areas of ground
which are each level in comparison with the dimensions of a and rough

V m

Fig. 3-22. —Atlantic entrance of the Panama Canal, with the docking facilities at Cristo¬
bal. Wavelength = 1.25 cm, 0.8° beam, altitude 1500 ft, radius 3 nautical mi. 9°21'N.
79°59'W.

in comparison with the wavelength, and which have the same reflection
coefficient K, reflect signals of equal intensity and must be distinguished
from each other through large-scale irregularities such as hills, structures,
and bodies of water. To make these large-scale irregularities most easy
to detect, it is desirable that the antenna pattern be smooth and properly
shaped to produce on the radar picture an even background against
which irregularities will stand out by contrast. The shaping of the

PROPERTIES OF RADAR TARGETS

[Sec. 3-14

antenna pattern is discussed in Sec. 2-5, where an expression for the
ideal antenna pattern is derived from an approximate expression for <r:

a = {Ra) (L) sin 0. (34)

In Sec. 2-5 it was assumed that L was a constant, and a comparison of
Eq. (34) with Eq. (33) shows this to be approximately true, since sec 0
differs appreciably from unity only for very short ranges. Based on
Eq. (34), the ideal antenna pattern is

G(8) = Go esc 2 6. (35)

A more exact expression, based on Eq. (33), is

G{6) = Go esc 2 6 \/cos 0. (36)

The effect of using an antenna whose pattern fits Eq. (35) rather than
Eq. (36) is to increase the strength of the signals at close ranges above
those at medium and long ranges. This increase is not large, amounting
only to 3 db at 60°; its main effect is to make the altitude signal stronger
than the succeeding ground signals. Radar experience indicates that the
specification of what curve the pattern should follow is less important
than the requirement that the pattern be smooth.

In Fig. 3-20 the diffuse bright rings at the center of the picture are
the result of an imperfectly shaped antenna pattern. These intensifica¬
tion rings 1 make it difficult to distinguish irregularities on the ground,
but they are not as objectionable as the black rings or “holes” which
would have appeared if the antenna pattern, instead of being too strong,
had been too weak in those regions.

Equations (30) and (33), combined, give only the average level S
of ground return. Particular signals vary widely. On the PPI, with a
medium gain setting, ground return can be seen to consist of many
bright signals. Among these bright signals are weaker signals, some
of them too faint to show on the screen. The resulting stippled or
“beaded” texture of ground return is clearly visible when fast sweeps
are used, as in Fig. 3-25. If the receiver gain control is set high, most
ground signals rise to saturation and ground return takes on the more
flattened texture seen in Fig. 317.

3-14. Mountain Relief. —The presence of hills and mountains in the
area covered by the radar presentation is indicated by the bright returns
from the mountain sides facing toward the aircraft and by the shadow
regions on the far side of the crests. These conditions follow directly
from the geometry of the illumination, and produce a very realistic

1 The rather diffuse rings of intensification should not be confused with the range
markers, which are narrower and appear at equal radial intervals out to the edge of
the picture.

Sec. 3-14]

MOUNTAIN RELIEF

effect of observing land forms in relief, although the radial illumination
from the center differs from the unidirectional illumination from north¬
west that is conventionally used in relief maps. Two illustrations of
this effect are shown in Figs. 3-23 and 3-24, the former obtained with a
3° beam at 3 cm, the latter with a 0.8° beam at 1.25 cm. Figure 3-23

Fig. 3-23.—Tokyo Bay, with Tokyo 21 mi east of the aircraft, at the head of the bay, and
Fujiyama to the southwest of the aircraft. Wavelength = 3.2 cm, 3° beam, altitude
30,000 ft, radius 50 nautical mi. 35°33'N. 139°14'E.

was observed roughly midway between Tokyo and Alt. Fuji, and shows
the characteristic shadow of the cone. Slightly to the southeast, Mt.
Echizen, less than half the altitude of Fuji, throws a semicircular shadow.
Many of the crests and valleys north of Fuji are identifiable by reference
to a map. In Fig. 3-24 the valleys formed by tributaries of the Sus¬
quehanna can be traced clearly in the relief.

It is often useful to visualize the radar presentation of the earth’s

PROPERTIES OF RADAR TARGETS

[Sec. 3-14

surface in terms of a small-scale relief model illuminated by a rotating
fan-shaped beam of light, with the source of light held above the model
at a height equivalent to the altitude of the aircraft. The direction
and shape of terrain shadows and the brightness of the near sides of the
mountains are properties of the radar picture which can readily be
understood through such scale models.

Fig. 3-24.—The Susquehanna River and its tributaries flowing through the Allegheny
Mountains near Jersey Shore, Pa. Wavelength = 1.25 cm, 0.8° beam, altitude 9500 ft,
radius 10 nautical mi. 41 G 19'N. 77°16'W.

As an aircraft approaches a hill or mountain, it will eventually (if
its altitude is greater than the height of the mountain) reach a position
where the farther slope is no longer hidden behind the crest. Although
the shadow is gone, it is still possible to distinguish the mountain on the
radar picture through the contrast between the brighter signal from the
near slope and the weaker signal from the far slope. In Fig. 3-24, for

Sec. 3-15]

STRUCTURES

example, the contours of the land are indicated partly by shading, partly
by true shadows. The identification of hills through intensity shading
depends largely upon the radar operator. There is a natural tendency on
the part of the operator to set the gain too high, raising all ground signals
to saturation and making small variations in intensity indistinguishable.

Fig. 3-25—Mouth of the Susquehanna River at Havre do Grace, Md. Buildings of
Edgewood Arsenal and Aberdeen Proving Ground are visible as bright patches south of the
electrified railway line. Wavelength 1.25 cm, 0.8° beam, altitude 4000 ft, radius 10 nautical
mi. 39°32'N. 76°13'W.

3T5. Structures. —The general appearance of structures and clusters
of buildings is illustrated in Fig. 3-25, which was obtained with a high-
resolution system in the region between Baltimore and Havre de Grace,
Md. The most prominent single feature is the curved line of the Pennsyl¬
vania Railroad. Bridges over two branches stand out in sharp contrast
with the water. Southwest of the position of the aircraft, near the

100

PROPERTIES OF RADAR TARGETS

[Sec. 315

periphery of the picture, the buildings comprising Edgewood Arsenal
are clearly visible; a similar group southeast of the aircraft corresponds to
Aberdeen Proving Ground. A third bridge over the Susquehanna
River, just north of the two visible in the picture, is barely suggested
by two bright dots at the upper end of the small island in the river.
In general, the three bridges appear as equally strong signals; in the
particular sweep corresponding to this photograph the third bridge
returned a poor signal.

Many structures stand out against ground return because they
project vertically above the surrounding level ground and intercept
energy intended for target areas behind them. The central portion of
the railroad in Fig. 3-25 is an example of a structure which casts a shadow.
Seen broadside from a relatively low angle, the wires and supports of
the overhead electrification system and the embankment upon which
the tracks are laid intercept energy and cast their shadows in the same

Fio. 3-26.—Increased angle intercepted by inclined target area. The length in range of a

pulse packet, A R, is \ct.

way as would a small hill or ridge. This type of contrast is less effective
when the target is viewed from a higher angle, for the same reasons that
make mountain contrast less effective at high angles of incidence.

Natural structures also show radar contrast. Examples are the rows
of trees that line canals and streams in otherwise treeless regions, the
hedgerows of Normandy and the cliffs of Dover, or the edges of forests 1
and the banks of rivers. As an illustration, Fig. 3-26 shows the increased
angle intercepted by a target area which spans a river bank. In Fig.
3-25, the bright line marking the east shore of the Susquehanna River is
characteristic of the strong reflections returned by sharply inclined river
embankments.

The radar signals received from man-made structures are often too
strong to be fully explained in terms of the solid angle intercepted by the
target. Figure 3-25 shows several examples of the bright signals from
groups of buildings, without accompanying shadows. In order to
account for contrasts as strong as those in Fig. 3 25 a certain amount of
rctrodircctivity in the target objects themselves must be present.

This retrodirectivity can arise in several ways. Strong specular

1 The near edge of a forest or group of trees gives a bright signal; the far edge gives
a weakened signal or casts a shadow.

Sf,c. 3 16]

CITIES

101

reflection will result whenever a flat surface happens to be oriented normal
to the line of sight; yet the mere presence of flat surfaces is not enough to
guarantee a strong reflection. If these surfaces were oriented in random
directions, the probability of finding one at just the right orientation
would be so low that the average signal from such a group of flat surfaces
would be no stronger than the average signal from a collection of isotropic
scatterers filling about the same volume. Therefore the flat surfaces
must be so oriented that the reflection is concentrated in the direction
of the radar receiver. In a group of buildings, a large proportion of the
flat surfaces will be vertical walls, while many others are smooth pave¬
ments or flat roofs. There are many opportunities for combinations of
three flat surfaces at right angles to form corner reflectors (Sec. 3-5),
which are highly retrodirective targets. The full potentialities of these
tremendous comer reflectors are never realized in practice because of
the strict tolerances imposed by the short wavelengths of microwave
radar. Insufficient flatness in the walls makes a huge, imperfect corner
reflector behave like one which is smaller but perfect. Inadequate
perpendicularity results in several return beams in the vicinity of the
aircraft instead of a single return beam pointed directly at the aircraft.
Nevertheless, the average effect of many triple corners is to provide
retrodirectivity in the radar target.

Vertical and horizontal surfaces can combine into double (rather
than triple) corners, giving directivity in elevation under certain con¬
ditions. It was shown in Sec. 2T2 that rough surfaces like the ground
can serve as satisfactory mirrors for more distant targets when the angle
of incidence is sufficiently low. Because double-comer directivity
depends on the mirror-like properties of a horizontal surface in front of
vertical structures, we should expect strongest signals from these struc¬
tures when they are seen from low angles. Many buildings or groups of
buildings return strong signals at long ranges but tend to fade at shorter
ranges when the higher angle of incidence reduces their retrodirectivity.
If the line of sight is nearly horizontal, strong signals are sometimes
observed by direct specular reflection from vertical surfaces without the
benefit of mirror reflection from an intermediate horizontal surface.

Special cases of target directivity in azimuth arise when, for instance,
large groups of buildings have parallel walls. The signals in directions
perpendicular to these walls are often intensified, as can be seen in
Fig. 3-35.

3T6. Cities.—The brightest signals within a built-up area (Boston,
Mass.) are presented in Fig. 3-27. This particular photograph was
obtained with a so-called “three-tone” presentation (Sec. 13-21), in
which gain and limit level are electronically switched back and forth
from levels most suitable for land-water contrast to levels giving the

102 PROPERTIES OF RADAR TARGETS [Sec. 316

best overland contrast for the brightest target highlights. In this
manner, the points yielding the brightest returns are presented over a
“base map” which shows the location of the aircraft and which partici¬
pates in any geometrical distortions of the radar presentation. Studies
of this type of presentation show that (1) the location of the brightest

Fio. 3-27.—Boston, Mass., with "three-tone” presentation (Sec. 13-21). Wavelength =
3.2 cm, 3° beam, altitude 4000 ft, radius 5 nautical mi. 42°20'N. 71°05'W.

signals changes from instant to instant, and (2) the great majority of
these highlights cannot be identified with any particular prominent
structures in the city. These bright signals, therefore, must be acci¬
dental strong reflections produced at random by favorable illumination
of particular surfaces and by constructive interference of reflections
from different surfaces within a signal pulse packet or target area.
“City return” is similar to ground return and sea return in that each

Sec. 3-16]

CITIES

103

signal represents the superposition of reflections from the surface ele¬
ments located within a region bounded by beam width and pulse length.
The individual targets, however, because of their low absorption and high
retrodirectivity, are more effective than the scatterers and irregularities
responsible for ground return and sea return.

Fig. 3-28.—The Kanto plain north of Tokyo. Wavelength = 3.2 cm, 3° beam, altitude
10,000 ft, radius 28 nautical mi. 35°59'N. 139°59'E.

In spite of the fluctuations of individual signals the average intensity
of the return from a city is sufficiently high to form a relatively stable
bright area on the screen. The shape of this area and the brightness of
particular sections remain sensitive to altitude and direction of approach,
but the whole group of signals is strong enough to give a reliable indica¬
tion under most circumstances.

The appearance of city signals of various sizes is illustrated in Fig.
3-28, a photograph obtained over the Kanto plain north of Tokyo. The

104

PROPERTIES OF RADAR TARGETS

[Sec. 3-16

urban area of Tokyo is a large group of signals near the southern limit
of the picture, with the industrial suburbs of Urawa and Omiya, north¬
west of the city, showing as a strong elongated signal. East of Tokyo
is Funabashi, a strong signal at the head of Tokyo Bay. Numerous
small towns in the Kanto plain are shown as individual arcs, particularly
to the west of the aircraft. The Tone River is visible just below the

Fig. 3-29. —Small towns near Worcester, Mass. Wavelength = 1.25 cm, 0.8° beam,
altitude 7000 ft, radius 24 nautical mi. 42°16'N. 71°48'W.

center of the picture, with the Toride railroad bridge appearing as a
strong signal just south of the aircraft.

Figure 3-29, taken at somewhat closer range with a system of higher
resolution, shows a number of small towns in the vicinity of Worcester,
Mass. A characteristic group of five bright signals appears near the
top of the photograph. The signal nearest the aircraft is a mountain
signal, readily identified as such by its triangular shadow. The remaining

CITIES

Sec. 3-16]

105

four signals represent the towns of Gardner, Fitchburg, Leominster, and
Ayer.

Figures 3-28 and 3-29 illustrate situations in which identification
depends on the recognition of particular groups or “constellations” of
towns; at long ranges the returns from individual towns lack distinctive

Fig. 3-30.—Part of the Connecticut River valley, with Springfield, Mass., to the north
and Hartford, Conn., to the south. Their shapes correspond roughly to the principal
built-up areas. Wavelength 1.25 cm, 0.8° beam, altitude 7000 ft, radius 20 nautical mi.
41°57'N. 72°39'W.

characteristics of their own, although at shorter ranges and with systems
of higher resolution such characteristics do appear. Fig. 3-30 shows
the cities of Springfield. Mass., and Hartford, Conn., observed at ranges
of about 10 miles with a 1.25-cm system. Here the bright returns form
characteristic shapes roughly corresponding to the densely built-up
parts of the cities. Intermediate conditions are illustrated in Figs. 3-31
and 3-32, which show two Japanese towns as seen with medium-resolution

106

PROPERTIES OF RADAR TARGETS

[Sec. 3-16

systems at short ranges. These towns had to be identified by reference
to other targets on sweeps of longer range, but the signals begin to show
characteristic shapes.

In almost all built-up regions additional information is contained
in the detailed brightness variations which become apparent at close
range. Many cities contain important and characteristic water areas.

Fig. 3-31. —Kanazawa, Honshu. Wavelength = 3.2 cm, 3° beam, altitude 10,000 ft, radius
10 nautical mi. 36°40'N. 136°40'E.

In Fig. 3-33 the bright region northwest of the center represents the
densely built-up area of Boston, Mass. The shape of the Charles River
Basin with its two vehicular bridges provides unmistakable identification.
A small dark patch slightly closer to the center corresponds to Boston
Common, and various water courses together with the shoreline provide
identification of various parts of the city. Figure 3 34 shows the further
detail which becomes visible at closer range. Figure 3-35 shows a

Sec. 316]

CITIES

107

portion of New York City in which immediate identification is possible
by reference to the Hackensack, Hudson, Harlem, and East Rivers,
together with Central Park and the various bridges.

It is sometimes possible to discern a few prominent features of the
street pattern of a city. A complete presentation of the street pattern
would be ideal, but present radar equipment lacks the resolution which

Fig. 3-32.—Obihiro, Hokkaido. Wavelength = 3.2 cm, 3° beam, altitude 12,000 ft, radius
15 nautical mi. 42°41'N. 143°12'E.

would make this possible. At very low altitudes and very short ranges,
major thoroughfares may occasionally be seen as dark lines in the bright
mass of city return. There is some evidence of the Manhattan street
pattern near the center of Fig. 3-35. Airport runways, which are
normally much wider than streets, can often be seen clearly at low alti¬
tudes, as in Fig. 3-21. On the other hand, the concentration of large
buildings along major streets and the presence of elevated railways or

108

PROPERTIES OF RADAR TARGETS

[Sec. 3 17

overhead trolley systems often results in a concentration of particularly
bright signals along such streets. The street patterns of Chicago and
Detroit, partially visible in Figs. 3-36 and 3 37, are of this type. Some
caution is necessary in the interpretation of such displays; bright radial
lines are occasionally caused by directionally selective reflection from a
mass of buildings with parallel surfaces. Such lines appear to move along

Fig. 3-33.—Outer harbor, Boston, Mass. Wavelength = 1.25 cm, 0.8° beam, altitude
8000 ft, radius 10 nautical mi. 42°18'X. 70°58'\V.

with the aircraft and can thus be distinguished from streets, which are
stable with respect to other signals.

3T7. Navigation.—Sections 3T2 to 3T6 have been devoted to dis¬
cussions of the kinds of targets and target contrasts encountered with
airborne radar. It remains to describe their integration into the radar
picture as a whole and the use of this picture as a navigational aid. A
fuller discussion of this subject will be found in Vol. 2 of this series.

Sec. 3-17]

NAVIGATION

109

Airborne radar is best used as a supplement to standard navigational
methods, rather than as a substitute for them. Overland navigation by
the traditional dead-reckoning procedure can be based upon determina¬
tions of ground speed and drift angle made by the radar operator through
measurements of the motion of ground targets, while the position of the

.. Jf

Fig. 3 34. —Boston, Mass. Detailed resolution of land-water boundaries permits direct
comparison with conventional maps. Wavelength = 1.25 cm, 0.8° beam, altitude 4000 ft,
radius 5 nautical mi. 42°21'N. 71°03'W.

aircraft is checked at intervals against a map by the identification of
radar landmarks along the route.

The characteristics of the radar system must be kept in mind when
flights are planned. Each radar set has its limitations in range and
resolution. The maximum range is limited by many factors, 1 including
the transmitted power, the receiver sensitivity, and the antenna gain.

1 See Chap. 2.

110

PROPERTIES OF RADAR TARGETS

[Sec. 3-17

The maximum range also depends upon the type of target and often
upon the altitude of the aircraft. Ground return, for example, reflects a
stronger signal at higher altitudes for the same reasons that make the
near side of a hill appear bright: a given area of ground intercepts a larger
solid angle and receives more of the incident radiation. Thus the range

Fig. 3-35. —Lower Manhattan, New York, and vicinity of Jersey City, N.J. Rivers,
bridges, and railway lines, together with the dark rectangle of Central Park, form an abund¬
ance of good reference marks. Wavelength = 1.25 cm, 0.8° beam, altitude 4000 ft, radius
5 nautical mi. 40°46'N. 74°01'W.

at which ground return and land-water boundaries can be distinguished
increases with altitude, provided the gain of the antenna is unchanged.

Large or highly retrodirective structures are usually visible to con¬
siderably longer ranges than is ground return. The difference in ranges
is well illustrated in Fig. 3-38, which was obtained with low gain adjust¬
ment at an altitude of 4000 ft over the Pennsylvania Railroad main line
in New Jersey. The land-painting range in this case extends approxi-

Sec. 3-17]

NAVIGATION

111

mately to the 5-mile range circle, while the strong reflections from the
overhead structure of the electrified railway line can be seen out to
10 miles. A higher gain setting would have resulted in increased ranges
both for structures and for ground return, with the maximum ranges
limited by the presence of noise on the picture.

Specification of maximum useful ranges for radar systems is difficult.

* * I

Fig. 3*36.—Chicago, Ill. Wavelength = 1.25 cm, 0.8° beam, altitude 4000 ft, radius 10
nautical mi. 41°52'N. 87°39'W.

The conditions for rigorous tests are so hard to establish, and the results
in general are accompanied by so many cumbersome qualifications, that
maximum-range figures have been controversial. Nevertheless, because
of the importance of range performance to radar navigation, a few rough
figures will be mentioned. At medium altitudes (10,000 ft), with air¬
borne radar systems designed for overland navigation and bombing,
ranges of about 40 (nautical) miles on ground return and about 100

112

PROPERTIES OF RADAR TARGETS

[Sec. 3-17

miles on large targets are observed with 3-cm systems such as the AN/-
APQ-13 and AX/APS-15, while with 1.25-em systems like the AX/APS-
22 the ranges available at present are about 15 miles on ground return
and 30 miles on large targets, for average atmospheric conditions in the
Eastern United States. Under conditions of high atmospheric humidity,

Fig. 3-37. —Detroit. Mich. The Ford Rouge River plant shows as a bright patch 7 mi
southeast of the aircraft. Wavelength = 1.25 cm, 0.8° beam, altitude 4000 ft, radius 10
nautical mi. 42°21'N. 83°01'W.

the absorption of energy by water vapor becomes an important factor
limiting the maximum range of a radar set at 1.25 cm (see Sec. 2-15).
Even strong signals from large cities are attenuated below noise level
if the cities are much beyond the maximum range for ground return.
Figure 3-39, which illustrates this uniform range cutoff, was obtained
with a 1.25 cm system at an altitude of 20,000 ft near the Pacific entrance
of the Panama Canal, with an average water-vapor concentration of

Sec. 3-17]

NAVIGATION

113

6.9 g/m 3 . Land-painting extends slightly beyond the 15-mile range
circle.

Some radar landmarks are more satisfactory than others. Routes
which run parallel to a coastline, a large river, or a range of hills are
more easily followed by radar than by contact flying with good visibility,
because radar eliminates effects of perspective. Other routes are easily

Fig. 3-38.—Main line of Pennsylvania Railroad near New Brunswick, N.J. Wave¬
length = 1.25 cm, 0.8° beam, altitude 4000 ft, radius 15 nautical mi. 40°22'N. 74°33'W.

followed if they are laid out with the selection of a few distinctive topo¬
graphical features along the way. A good radar target like a lake may
nevertheless be an unsatisfactory radar landmark if there are other lakes
in the same region, with which it might be confused. The choice of the
best landmarks varies with the radar system, as well as with the terrain.
When the radar system has high resolution but a short range or a small
field of view, the detailed character of a target is relied on for identifica-

114

PROPERTIES OF RADAR TARGETS

[Sec. 3-17

tion, while with systems of less resolution but greater range it is often
the spatial relationship of a group of targets which results in their
identification.

In mountainous regions the presentation of a given area varies con¬
siderably with the altitude and position of the observing aircraft, and
skill is required in using radar pilotage over this sort of terrain. How-

Fig. 3-39.—Pacific Coast near Balboa, C.Z. Average water-vapor concentration over
flight path 6.9 g/m\ Wavelength = 1.25 cm, 0.8° beam, altitude 20,000 ft, radius 23
nautical mi. 9°01'N. 79°35'W.

ever, the Fifteenth Air Force of the U.S. Army has used the method
extensively in navigating across the Alps. One difficulty inherent in
the use of radar pilotage over mountainous terrain is illustrated in
Fig. 3-40. West of the aircraft a mountain chain rising to 6000 ft throws
long shadows into the Mogami Valley beyond. The town of Yamagata
is seen as a bright signal beyond a spur of Mt. Taki extending northwest

Sec. 3-17]

NAVIGATION

115

from the main range. If the aircraft had been slightly south of the
position shown here, this town would have been completely obscured by
the long shadow visible just south of it in the picture. Such situations
can be foreseen by intelligent map analysis and routes chosen to minimize
the difficulty.

Airborne radar is particularly valuable when navigational emergencies

Fig. 3-40.—Sao Mountains, northern Honshu. Wavelength = 3.2 cm, 3° beam, altitude
10,000 ft, radius 30 nautical mi. 38°09'N. 140°38'E.

occur. The reorientation of an aircraft that is off course or the location
of an airport for an emergency landing may depend upon the radar sys¬
tem and upon the ability of the radar operator to interpret adequately
the brightness pattern on his oscilloscope. Timely notice of the location
of thunderstorms is given on the radar screen. The most graphic warn¬
ing of all is the black shadow extending to the edge of the radar picture,
cast by a mountain whose summit rises high enough to threaten a crash.

CHAPTER 4

LIMITATIONS OF PULSE RADAR

By E. M. Purcell

To a thoughtful observer, one of the most striking features of a
microwave radar screen is the quantity of information that is available
at a glance and continually being renewed. In some installations the
map of an area of many thousands of square miles is drawn every few
seconds. Such a map may comprise in effect some 10 s to 10 6 separate
“elements” of information similar to the elements from which a tele¬
vision picture or a half-tone cut is constructed. This in itself is no cause
for complacency; an ordinary photograph, recorded in a fraction of a
second, usually contains much more information. Indeed, the unini¬
tiated, comparing the rather fuzzy radar picture with the pin-point detail
of the photograph, may conclude that the obvious deficiencies of the
former merely betray the primitive state of the art, and that vast improve¬
ment in distinctness of detail is to be expected in the normal course of
development. These conclusions are only partly true. In the first
place many of the unique capabilities of radar, such as direct range
measurement or detection of very remote objects despite cloud and dark¬
ness, often deserve more emphasis in radar design than does the ability
of the set to produce a lifelike picture. In the second place, the pulse
radar process is subject to certain inherent limitations. These limitations
are of obvious origin. A few have been mentioned already in preceding
chapters, but since the interest there was merely in the detection of
energy reflected from a single target and not in over-all radar system
design, their implications were not pursued.

4T. Range, Pulse-repetition Frequency, and Speed of Scan.—It is
the function of most radar sets to search continually through some region
in space by scanning. Naturally the radar designer strives always to
enlarge the region which can thus be searched, to increase the rapidity
with which it can be completely explored, and to improve the ability to
distinguish detail within the region. In this endeavor he is made
acutely aware of two of the fundamental limitations of pulse radar which
can be blamed respectively on the finite velocity of light and the necessity
of funneling all information in sequence through a single electrical
channel. The effect of these two limitations and the close connection
between them can be seen in a simple example.

116

Sec. 4-1]

RANGE, PRF, AND SPEED OF SCAN

117

After each pulse transmission enough time must be allowed for energy
to travel to, and return from, the most distant targets, the time required
for range R being 2 R/c, or nearly 11 /nsec for each statute mile of range.
If it is supposed that a radar set operates with a pulse-recurrence frequency
of 500 pps, during the 2000-/asec interval following each pulse echoes
will be received from objects within a range of 186 miles. A target
250 miles away may, however, return a signal strong enough to be
detected. If it does, this signal will arrive 690 psec after the next trans¬
mitted pulse, in exact imitation of an echo from a target at 64 miles
To decide how serious a complication the possibility of a “second time
around echo,” as it is called, presents, two cases must be carefully
distinguished.

1. Targets beyond 186 miles are not of interest. The second-time-
around echo is a nuisance only. It would be well to get rid
of it if there were some way to do so; if there is not, it would be
desirable to identify it as an interloper.

2. The extension of coverage beyond 186 miles is for some reason
important. Echoes from targets beyond that range constitute
valuable information that ought to be sorted out and presented
unambiguously.

If Case 1 applies, the difficulty can hardly be regarded as funda¬
mental. For one thing, there are several ways in which the echo in
question can be identified as originating from the preceding pulse. The
use of a slightly irregular pulse-recurrence rate, for instance, will prevent
overlapping of successive echoes of this type from the same target,
without affecting the superposition of echoes from a target lying within
the range limit defined above. If a more powerful remedy is needed, the
unwanted echoes can be removed altogether by some such scheme as
the following one. The frequency of the transmitter may be changed for
each pulse, with a corresponding shift in the frequency of the local
oscillator of the receiver. For example, the transmitter frequency—
that is, the carrier frequency—might alternate between two values, f\
and / 2 , separated by a frequency interval greater than the receiver pass
band. Echoes originating from the first transmitted pulse, at frequency
/ 1 , would not be amplified if received during the interval following the
second pulse, for during this interval the receiver would be in tune only
for echoes of frequency / 2 , and so on. This rather clumsy expedient,
although it is actually feasible, would scarcely be justified solely as a
means of avoiding a reduction in pulse-repetition frequency. It is men¬
tioned only to show that objectionable second time around, or even
“nth time around,” echoes could be eliminated if necessary without
reduction in PRF and without a drastic change in the radar process.

118

LIMITATIONS OF PULSE RADAR

[Sec. 4-1

The situation is different in Case 2, for if it is required to receive both
first- and second-time echoes, to separate out the latter, and to present
them in proper relation to a range scale, some method must be used
which is the equivalent of operation on two or more frequency channels
simultaneously. Various schemes to circumvent such operation may
occur to the ingenious mind, but close examination will show that each
is either tantamount to multichannel operation 1 or involves some sacrifice
in performance through an abnormally wide pass band, incomplete use
of available time, or the like.

Supposing that the reader accepts, with more or less reservation, the
force or the range-PRF restriction, we proceed with the example, in
which the PRF is 500 pps and the range limit is accordingly 186 miles.
Suppose that the width of the radar beam in azimuth is effectively 1°,
and that the operation required is a search through 360° in az.muth by
rotation of the antenna. Clearly, if the antenna turns at a rate exceeding
500° per sec, during one revolution some narrow sectors in the region to
be covered will fail to be illuminated. We therefore conclude that the
shortest possible time in which the area can be searched is fUj} or 0.72
sec. If the rate of rotation were much faster than 1/0.72 sec or 1.4 rps,
a retentive screen could be used to accumulate information over several
revolutions until all gaps were filled, but the time for collecting a complete
picture would again be 0.72 sec or longer.

As a matter of fact, rotation at a rate higher than 1.4 rps is ruled out
by quite another consideration. In order to receive an echo from the
target, the antenna must point toward the target with an accuracy
measured by the beam width. At a speed of 1.4 rps, in the present
example, this requirement is already jeopardized since the antenna will
have rotated through just 1° between the transmission of a pulse and the
arrival of the corresponding echo from a target at the range limit.

The extreme limiting conditions which have been assumed allow any
target to be struck by one pulse of energy, at most, within the time of one
complete searching cycle, or scan. In Chap. 2 it was pointed out that
the minimum detectable signal power depends sensitively on the number
of echoes from the same target which can be accumulated and integrated.
The reduction in S m „ purchased at the price of increased scanning time
by allowing the beam to dwell in the target for several pulse intervals, is
almost always worth the cost.

The number of pulses striking the target during one scan is an impor¬
tant parameter in radar design which will reappear frequently in later

1 The use of different directions of polarization as a means of distinguishing one
arriving signal from another suggests itself immediately. This would be an effective
and elegant method for operation on two channels with common antennas were it
not that radar echoes, in general, are substantially depolarized.

Sec. 4-1]

RANGE , PRF, AND SPEED OF SCAN

119

chapters. This number will be denoted by JV„ and defined, where exact
specification is required, by the relation

N m = til (1)

Uae

In Eq. (1), v, is the pulse-repetition frequency, 0 is the width in radians
of the radar beam, between half-gain points as usual, and is the angular
velocity of scanning in radians per second. Of course N is closely
related to the more general and more loosely defined quantity n, intro¬
duced in Sec. 211. If N m is required to be, for example, 10, the rate of
rotation of the antenna in the previous example must be restricted to
0.14 rps or about 9 rpm. 1

The numbers arrived at in this example are typical of long-range
ground-based microwave radar. Any considerable improvement in all
three characteristics—range, scanning speed, and angular resolution—
will be blocked by irreconcilable requirements as long as a single radar
set is relied upon for the entire coverage. But the restriction falls
even more severely on radar systems designed to search rapidly in two
angular coordinates rather than in one.

Suppose that it is our ambition to design a radar system which will
locate in azimuth, elevation, and range any aircraft within 20 miles
with the angular accuracy that can be achieved through the use of a
beam 2° wide in both azimuth and elevation. The solid angle which
the beam itself includes is roughly 0.001 steradians whereas the hemis¬
phere to be searched represents a solid angle of 27r. Some 6000 “ patches ”
in the sky must therefore be covered. The number of radar pulses
needed during a complete scanning operation, regardless of the order
in which it is carried out, cannot be less than 6000 N. c . The maximum
pulse-recurrence frequency consistent with a 20-mile range 2 is about
4500 pps. Hence the minimum time for completion of the scanning
operation is 6000A r „/4500 or 1.3JV.„ sec. Even if N*, is permitted to
be as small as 3, for a complete picture a scanning time of 4 sec is required,
which for many purposes is uncomfortably long.

The only physical constant which has been invoked in the foregoing
discussion is the velocity of light. The only assumption which has
been made about the radar system amounts to this: There is only one
channel, through which elements of information in the form of echoes

1 It should be noted that imposing this restriction incidentally insures that the
antenna will not turn too far away from the direction of the target before the echo
returns.

2 Certain practical considerations which prevent the use of the entire interval
between pulses for reception of signals and which therefore set the limit on v, even
lower than c/2R (see Chap. 12) are here ignored.

120

LIMITATIONS OF PULSE RADAR

[Sec. 4-1

move in single file. It must be concluded that the restriction which
thus arises can be overcome only by the use of multiple channels. The
simplest—at least in conception—and the most direct way to do this is
to use two or more radar systems, apportioning to each a part of the
region to be covered.

This method is not the only practical scheme for multichannel
operation. In fact, in one of the most important existing applications of
multichannel operation, the “V-beam” radar, an increase in the amount

Fio. 4-1.—Principle of V-beam height measurement.

1. Plane of Beam I is vertical. Plane of Beam II falls back 45° from Beam I. Ground

edges of both beams are common at K.

2. As both beams rotate together, target T is picked up in Beam I when ground edges of

both beams are at K.

3. Target T is later picked up in Beam II when ground edges of both beams are atK'.

4, The angle formed by the advancement of the ground edges from K to K' (A0)
depends on the angle 6 of elevation of the target T.

of information provided is achieved in a more subtle and, under the
circumstances, a more effective way. The V-beam principle permits
a single scanning radar to give height as well as range and
azimuth of aircraft. In addition to the vertical fan beam which is char¬
acteristic of microwave search radar (cf. Chap. 15), the V-beam set
provides an additional fan beam that is rotating at the same speed and
the plane of which is tilted out of the vertical. If the azimuth and range
of a target are known from the first beam, the height can be inferred
from the time of appearance of the same target in the second, or “slant”
beam (see Fig. 4T). This latter beam is associated with a completely

Sec. 4-2]

POWER AND INFORMATION RATE

121

separate transmitter and receiver. The V-beam radar is thus an authen¬
tic example of the use of a separate radar system to overcome a scanning
speed limitation.

In a certain sense, however, the use of the second channel in this
way more than doubles the number of angular elements searched in a
given time. That is to say, an isolated target can be located in azimuth
and in elevation with an accuracy that would ordinarily require a sharp
“pencil” beam. But to scan the whole region with such a pencil beam
would take, according to the earlier discussion, a very much longer time.
It might therefore appear that the V-beam system eludes the very
restrictions which have been claimed to be fundamental. This is to be
explained by the fact that the V-beam height-finding method works
only if relatively few targets appear on the screen at one time; otherwise
there is essential ambiguity in the interpretation of the picture. The
system is, therefore, not fully equivalent to a pencil-beam scan of the
same angular region.

Actually more than two separate radar sets are involved in the
V-beam system, for both the vertical and the slant beams are themselves
composite. This, however, has nothing to do with the scanning speed
limitation, but is required merely to get adequate range and vertical
coverage. It is a consequence, in other words, of the radar equation
for fan beams discussed in Sec. 2-5.

4-2. Bandwidth, Power, and Information Rate. —If a radar system
were used to find only the direction of a target, range information being
suppressed, it would be operating very much like a television camera.
The picture so obtained would, in effect, be divided into a number of
elements equal to the ratio of the total solid angle scanned to the solid
angle included in the beam itself. Thus the number of pieces of informa¬
tion that the system can collect per second is simply the number of
picture elements multiplied by the number of complete scans per second,
exactly as in television. In the radar system giving hemispherical
coverage which was used as an example in the preceding section, this
number comes to 1500 elements per second, which is not very impressive
by television standards. The type C indicator already mentioned in
Sec. 211 and described in more detail in Sec. 6-6 gives information of
just this sort. It has not found wide use for two reasons: (1) the accom¬
panying increases in minimum detectable signal power, explained in
Sec. 2-11, and (2) the fact that the method discards a large fraction of the
information available in the radar system, the range information.

An even closer approach to the television method has been visual¬
ized, in which the proposed radar receiving system is built something
like a television camera. A mosaic of microwave-sensitive elements
located at the focal surface of a receiving antenna would be scanned by an

122

LIMITATIONS OF PULSE RADAlt

[Sec. 4-2

electron beam. The system would be handicapped by the limitation
on angular resolution imposed by wavelength and antenna aperture,
but it should be said that the possibilities of storage inherent in the
mosaic method might eventually offset to some degree the other apparent
disadvantage of the system—its low sensitivity. As usual in c-w radar,
knowledge of target range would not be afforded by such a system
without further elaboration.

If range is taken into account, the rate at which the radar collects
information can be computed in a very direct way. Under ideal cir¬
cumstances (use of entire interval between pulses, PRF consistent with

Fig. 4-2. —Analysis into pulse packets of the region scanned. Note that the pulse-
packet, which defines a volume from which echoes are received simultaneously, is only half
as long as the outgoing wave train.

range limit, and adequate bandwidth in both video amplifier and indica¬
tor system), the rate at which information of all types is collected is
simply the rate at which separate echo pulses can be received. This
rate would normally be about 1/r, diminished by the factor 1 /AT which
takes account of repetition of pulses from the same target. 1 This
number, 1/r AT, is correct no matter how the information is divided
between angular coordinates and range coordinates. The same result
can be obtained by observing that the radar system analyzes a, region
in space by dissecting it into elements of volume, so-called “pulse

1 To be sure, repetition of pulses from the same target does give extra information
in that it helps to distinguish a weak echo from noise. In this section, however,
sensitivity is not the primary concern, and it has been tacitly assumed that the echoes
appearing on the radar screen are all well above the noise background.

Sec. 4-31

PULSE RADAR AND C-W RADAR

123

packets,” whose dimensions are determined by the angular size of the
beam together with the radial distance cr/2. If 0 (see Fig. 4-2) is the
total solid angle scanned in a particular case, to the solid angle included
in the beam, and T the total scanning time, it is necessary to apply the
restrictions discussed in the previous section which require that

T _ UN,, _ N, c n 2 R

tor, to C

On the other hand the number of pulse packets in the volume scanned
is (U/u)(2R/ct). Hence the number of separate volume elements
examined per second is

Q 2R 1 1

to cr T tN , c

( 3 )

Since the pulse duration t and the bandwidth (B of the radar receiver
are ordinarily related approximately by (B = 1/r, it can also be stated
that the rate at which elements of information are collected is of the
order of magnitude of the bandwidth (B. This conclusion, which has
been approached by a roundabout way, is familiar to the communication
engineer, whether he is concerned with voice, facsimile, or television
transmission.

Let us see how closely a typical radar system approaches this funda¬
mental limit. Consider an airborne ground-mapping radar with a 1.5°
beamwidth and PRF of 1800 pps, scanning at 15 rpm. Suppose that
the pulse duration is 1 /xsec and that a region 30 miles in radius is mapped
on the indicator screen. By a little arithmetic it is found that N„ is
30 in this case and that the number of separate patches on the ground
that are examined in 1 sec is 18,000. The product of these numbers,
540,000, is to be compared with the bandwidth of the system described,
which would probably be about 2 Mc/sec. The important point is
that the numbers do not differ by orders of magnitude. It must be
said, however, that it is not always easy to make full use on the indicator
of the information available in the radar system (cf. Secs. 13-20 and
13-21).

4-3. Pulse Radar and C-w Radar.—The last section has a bearing on
the relative capabilities of pulse radar and so-called “c-w radar,” by
which is meant a system operating at relatively low peak power, with
a very narrow receiver pass band, and making use of the doppler prin¬
ciple, or of frequency modulation. As was explained in Sec. 2-9, a
reduction in pulse power, accompanied by a corresponding increase in
pulse length and decrease in receiver bandwidth, leaves the maximum
range of a radar system unaffected. Proceeding to a limit in this direc¬
tion, imagine the pulse to be made so long that it fills the whole interval,

124

LIMITATIONS OF PULSE RADAR

[Sec. 4-4

1/jv long, which previously separated successive pulses. At the same
time the average power is kept constant by a reduction in pulse power
by the factor tv t . The receiver bandwidth, meanwhile, is reduced to
about v r cps. The result is essentially a c-w system in so far as power and
sensitivity are concerned, with a bandwidth of v r . It can see as far as
the previous radar system, but it cannot see as much in the same time.
Unless it is provided with multiple channels it can collect information
only at the rate v r .

The reader must be cautioned against taking too literally the result
of the above argument, for the hypothetical variation of system param¬
eters cannot be duplicated in practice. A change in pulse power, by a
large factor, entails a change in the type of tube used as a transmitter,
and perhaps in other components as well. The radar designer, in other
words, cannot adjust pulse duration arbitrarily, keeping average power
constant; nor can the receiver pass band be made arbitrarily narrow
as t is increased, for effects such as fluctuations of the echo eventually
impose a limit. This problem will be discussed in detail in the following
chapter which is concerned specifically with c-w radar. The general
conclusion, however, remains valid—an essential advantage of high
pulse power, as used in pulse radar, is that it permits information to be
obtained rapidly.

For certain tasks, no very high information rate is required, and for
such applications the various c-w methods (Chap. 5) deserve considera¬
tion. In the problem of the radio altimeter, for example, what is required
is merely the range of a single, large, ever-present target—the earth below.
It is significant that the most important practical application of c-w
radar has been made in this field.

4-4. Clutter. —One of the most formidable limitations to the useful¬
ness of pulse radar until recently was that imposed by “clutter.” Often
a radar system sees too much, rather than too little; the picture is con¬
fused by unwanted echoes, or clutter. This can be made up of echoes
from surrounding objects on the ground (ground clutter), of echoes from
the irregular surface of the sea (sea clutter), or even of echoes from storm
clouds. The problem is to find the desired echo in the midst of the
clutter. Although various palliatives have been invented (Chap. 12)
which accentuate a fairly strong echo relative to a diffuse background of
clutter, this difficulty is plainly fundamental as long as there is no essen¬
tial difference between the echoes that make up the clutter and the echoes
from what we may choose to call the true target. How can the radar
system distinguish between the echoes from boulders, ridges, trees, and a
multitude of irregularities on the side of a hill, and the echo from a tank
moving down the hill? How can the periscope of a submarine be seen
against the background of echoes from a considerable area of rough water?

Sec. 4-4]

CLUTTER

125

How can a low-flying plane be tracked across a radar map filled with
“permanent” echoes?

The only basis that is known for a distinction between the echoes
from a particular target and equally strong echoes from its immediate
surroundings is the motion, if any, of the target relative to its surround¬
ings. 1 The reflection of a wave by a moving object gives rise to a signal
as received in the neighborhood of the (stationary) transmitter, which
differs slightly in frequency from the outgoing wave. This is the familiar
doppler effect. The frequency difference A/ is but a small fraction of
the original frequency in the case of electromagnetic waves, being in
fact (2v/c)f„ where v is the velocity of the target along the line of sight
and c the velocity of light.

Doppler detection systems, or “c-w radar” as they are sometimes
loosely called, utilize this principle. In fact the doppler effect and c-w
radar were from the beginning so closely identified as to create a rather
widespread impression that pulse radar was inherently incapable of
capitalizing on this essential difference between fixed and moving targets.
This is not true, fortunately, as has been vividly demonstrated by the
development of methods, described in Chap. 16, which make possible a
distinction between moving targets and their surroundings. In some
cases the echoes from the latter are automatically rejected.

This is a spectacular advance in pulse-radar technique but it does
not entirely eliminate the clutter problem. It is applicable only to
moving targets, and then only when the unwanted echoes from the sur¬
roundings do not fluctuate so rapidly as to defeat the pulse-to-pulse
comparison which is an essential part of the scheme.

Another direction from which the clutter problem can be attacked
is that of resolution. To just this quality is due the great advantage of
microwave radar over long-wave radar in respect to clutter. As the
radar beam is made narrower and the pulse shorter, the amount of
clutter signal superimposed on the target signal decreases. Also,
improved resolution often allows recognizable forms to be distinguished
in the radar picture. A road or a river may be plainly discernible on a
radar map even though any one of the many traces making up the picture
would be undecipherable. How far we can hope to go in improving
resolution depends on factors already discussed, namely the beamwidth-
aperture-wavelength relation, considerations of scanning speed, and the
practical limits on pulse length and range resolution. Within these
limitations, however, there is still much room for development.

1 One exception to this statement must be made. Echoes from spherical water
drops (rain clutter) accurately preserve the polarization of the incident wave, and it
has been demonstrated that rain clutter can be almost entirely eliminated by making
use of this fact (Sec. 310).

126

LIMITATIONS OF PULSE RADAR

[Sec. 4-4

The reader may well ask whether a phenomenon has been overlooked
which could be used to distinguish some targets from others. There
appears to be no possibility for such a phenomenon in the elementary
process of reflection of electromagnetic waves from inhomogeneities
in the medium through which they travel. A returning wave is char¬
acterized by frequency (including phase), intensity, and polarization.
If two targets within the radar beam—for example, a telephone pole and
a stationary man—produce echoes similar in the respects listed, they are
utterly indistinguishable, as much as we might prefer to label one clutter
and the other the true target. Such echoes may very well be identical
in the respects listed since no significant difference exists at these fre¬
quencies between the electromagnetic properties of a man and those of a
piece of wood. To put it another way, the dimension of “color” is not
available because the radar cross section of most objects varies in no
systematic way with frequency. Distinction by shape, on the other
hand, is possible only when the radar beam is considerably smaller in
cross section than the object viewed.

CHAPTER 5

C-W RADAR SYSTEMS

By W. W. Hansen

6-1. General Considerations.—We shall begin with a discussion that
is fundamentally useful in understanding what follows, but has as its
immediate object a definition of the scope of this chapter more precise
than is given by the chapter title.

The simplest conceivable radar system consists of a source of r-f
power, an antenna, and a scattering object or target. The antenna
emits waves with time factor c" 1 , which, on striking the target at a
distance r, are reflected and returned to the antenna, where their time
factor will be e i< “‘~ 2kr) with k = 2ir/X. The returned waves will be
reduced in amplitude by a factor a which depends on the target and
various geometrical factors, as discussed in Chaps. 2 and 3.

This returned wave will give rise to currents and voltages in the
antenna, which add to those produced by the power source and so give
rise to a voltage-current ratio, or impedance, which is changed from the
value existing when no target is present.

In principle, this impedance, or some similar quantity, might be
measured on an absolute scale, and the deviations from the normal, or
no-target value, ascribed to the presence of a target.

Practically, this procedure is impossible because the returned signals
are often 10 -9 times as large, on a voltage basis, as the outgoing signals,
with the result that the variations in impedance might be of the order
of a part in 10 9 . Such variations can hardly be measured in the labora¬
tory at low frequencies, let alone in the field and at microwave frequencies.

It is therefore necessary to cause the returned signals to vary in some
manner so that the variation can be measured, rather than to attempt
such an absolute measurement as that described above.

This desired variation is caused by a modulation process of some sort.
The word “modulation” is used here in a general sense to include changes
induced by the target as well as changes in signal introduced at the
transmitter. All possible radar systems can then be classified by describ¬
ing the type of modulation and the use made of the resulting information.

As a specific example of these general remarks, let us take a very
simple radar system which consists, as shown in Fig. 5T, of an r-f power
source, an antenna, a rectifier, a high-pass filter, an indicator, and a

127

C-W RADAR SYSTEMS

128

[Sec. 5-1

target. It is assumed that the target is moving radially, thus supplying
the needed modulation.

In consequence of the radial motion of the target, which we suppose
to be at constant velocity v r , the phase of the returned signal, relative

Fia. 51.—Simplest possible radar system, using single transmitted frequency, with
modulation derived from target motion.

to the outgoing one, shifts continuously. In other words, the returned
frequency is different from the outgoing frequency, the difference being
(2 v r /c)f with v r the radial velocity and c the velocity of light.

Numerically, with v r in mph and / defined by a wavelength X in cm,
the frequency difference, which is called the “doppler frequency,” is

given by

fa = 89.4 ^ r , (1)

or, at 10-cm wavelength, f D amounts roughly
to 9 cps/mph. The doppler-shifted return

signal, when added to the transmitter voltage
and rectified, gives rise to a voltage with
small pulsations recurring at the doppler fre¬
quency. The steady component is removed
A ~ / — by the highpass filter, which may be simply

FlG - 5 2 ' . Thc u . ppcr d ! a ~ a transformer or a series condenser. The

gram shows the single rourier

component / 0 radiated by the fluctuations are amplified and used to actuate

transmitter; the lower shows ^e indicator. Thus the presence of a (mov-

the components present in the g t

receiver, these being /o from ing) target IS detected.

the transmitter and f« ± }d Although the system i ust described is hardly

from the target. . ° . ,, ,, .

practical, apparatus working on exactly this

principle but with slight technical modifications can be useful.

In Fig. 5-2 such a system is described diagrammatically in terms of
type of modulation and use made of the returned signal. The upper
part of the diagram shows the amplitude of the Fourier components
radiated by the transmitter; the lower part shows the amplitude of the

Sec. 5-2]

TRANSMITTED SPECTRA

129

components present in the receiver. The modulation is produced by
target motion, and the system makes use of this modulation by deter¬
mining the presence or absence of a signal of doppler-shifted frequency,
and usually also, by giving some indication of the magnitude and possibly
the doppler shift of this signal.

6-2. Transmitted Spectra. —Consider now a radar system of a general
type, as described from the Fourier-analysis point of view, either by a
diagram such as Fig 5-2 or, more precisely, by a Fourier series (or
integral) for some transmitter voltage or current. Such a series might be
written as

and we know that if &j„ = nu, such a series can represent any periodic 1
function. This series is sufficiently general—in fact, that is the difficulty.
The series contains more information
about the transmitted signal than is
commonly available.

To make use of Eq. (1) we must
therefore relate the different a n with
various known quantities. A precise
and complete connection for all pos¬
sible forms of modulation might well
occupy a book, but sufficient infor¬
mation for present purposes is con¬
tained in the brief series of statements that follow.

In the amplitude-modulation case the signal generally consists of a
carrier of angular frequency a>o, which is modulated at a frequency asso¬
ciated with the repetition rate. Thus = too + nu r and we have a
carrier wn and a number of evenly spaced sidebands, as shown dia-
grammatically in Fig. 5-3, which shows a spectral distribution resulting
from a sequence of pulses. Of course the signal is not strictly periodio
unless o) 0 chances to be an integral multiple of co,.

The sidebands have significant amplitude over a range that depends
on the pulse width, being approximately 1/r on a frequency scale. Thus
the number of important sidebands is roughly l// r r or T,/t. As is

1 The voltages in radar systems are often, and even usually, not really periodic—
there is no phase relation between the various pulses. We choose to simplify the
situation by ignoring this fact. Ordinarily no harm is done, for in f-m and doppler
systems, voltages are periodic, and in normal pulse systems the relative phases from
pulse to pulse are ignored. In the special form of pulse system known as the “MTI
type” (Chap. 16) the voltages are not actually periodic, but special relations between
receiver and transmitter combine to give the same effect.

Fig. 5-3.—Approximate frequency
spectrum of a sequence of pulses of carrier
frequency fo, repetition Irequency f r , and
duration r.

130 C-W RADAR SYSTEMS [Sec. 5-3

pointed out in Chap. 4, 1/r is also the maximum rate at which information
can be received.

When frequency modulation is used, the variation of a with w depends
on the form of modulation just as it depends, in the amplitude-modulation
case, on the pulse shape. Usually the frequency is varied either (a)
sinusoidally or (b) in a sawtooth manner. The results are shown qualita¬
tively in Figs. 5-4a and 5-4 b, which are drawn for the normal case in which
the frequency deviation is large compared to the modulation frequency.
Also, only the envelope of the |a„| has been drawn. The actual |o„j fluctu¬
ate irregularly below this value.

For pulse modulation, the phases
are such as to make the component
waves add to a maximum periodi¬
cally. For example, if one pulse is
centered on time t — 0, the phases
are all zero. In the frequency-mod¬
ulation case, the phases are such
that the various components add to
give a result that varies more or less
sinusoidally with time, but with con¬
stant amplitude.

Of course there are many possible
types of modulation besides simple
AM and FM but these will not be
treated here.

5-3. Effect of Target.—The effect
of reflection from the target on this
spectrum will now be considered.
First, all amplitudes are greatly re¬
duced, as is discussed in detail in
Chap. 2. Second, the scattering
cross section of the target is, in
general, a function of a>; the various
amplitudes are therefore not equally reduced. This effect can be
expected to be notable only when the target extent is comparable to c
divided by the bandwidth. Third, there is a phase change, linear in u,
with proportionality constant depending on the distance. Fourth, all
frequencies are shifted by the doppler frequency. Finally the scattering
cross section varies with time; this introduces an additional modulation
which broadens each of the returned sidebands by an amount depending
on the rate of the fluctuation. (All this is for a single target. Usually
there are many targets, in which case the above specification is further
complicated by a summation over all targets.)

Fig. 5-4. —Approximate frequency
spectra for frequency modulation, (a)
with sinusoidal and (fc) with linear saw¬
tooth variation of instantaneous fre¬
quency. More precise figures would
show a few sidebands outside ^/, the
maximum frequency deviation, and the
intensities of the various sidebands as
fluctuating irregularly about the mean
value here shown.

Sec. 5-4]

CLASS OF SYSTEMS CONSIDERED

131

Such, then, is the information potentially available to the receiver
of a radar set. The amount of this information, which varies with set
type, may be enormous, and use is seldom made of all of it. We may
complete our classification of possible radar types by specifying what
use the receiver makes of this information. For example, in a radar
of the usual pulse type, the linear phase change in going from com¬
ponent to component of the returned waves may be just compensated
by an increased time. As a result, the returned waves add to a maximum
at a time later than do those in the outgoing spectrum. This time delay,
which is the observed quantity, may then be regarded as a measure of the
rate of change of phase with frequency of the returned components.

6-4. Class of Systems Considered. —In this chapter we will consider
that class of systems in which the modulation is such that energy is
emitted all, or nearly all, the time. Quite arbitrarily, we take “nearly
all” to mean at least 10 per cent of the time—a large percentage in com¬
parison with that usual-in pulsed radar, where energy is generally emitted
during less than 0.1 per cent of the time. In Fourier terms this may
mean, in the case of frequency modulation, almost any bandwidth but
phases such as to give constant amplitude. Or, when amplitude modula¬
tion is employed, it means that there are, at most, 10 significant side¬
bands. There may exist only the carrier, as in the simple system
described in Sec. 5-1, where the modulation is provided by the target.

In considering systems of this type, we will first describe a number of
specific systems and for each system the relevant theory, leaving any
generalizations until the end of the chapter. This appears to be the
only feasible course since of many possible systems few, if any, will be
familiar to the average reader, and general theory would therefore be
scarcely comprehensible.

The reader should be warned that in the descriptions of these specific
systems quantitative information will be lacking on various points,
even on important ones. For example, in the first system discussed,
the aural detection of doppler frequencies in the presence of hiss noise is
employed. Various questions immediately arise that are similar to those
treated in the last part of Chap'. 2. Here they are not treated—adequate
information simply is not available. This situation and others like it
are the result of the fact that very little research has been done on c-w
systems in comparison with that devoted to pulse systems.

There are various reasons for this comparative neglect of c-w problems,
one of which is certainly valid. All the c-w systems to be described
have only a small effective receiver bandwidth (as explained in Chap. 4)
and, therefore, a limited rate of information transmission. Obviously
this is true for amplitude-modulation systems with 10 sidebands or less
and with sideband spacing fixed (see Chap. 4) by the maximum unam-

C-W RADAR SYSTEMS

132

[Sec. 5 6

biguous range, and it will appear later to be true also of frequency-
modulation systems.

5- 5. Utility of C-w Systems. —In spite of the fact that c-w systems
are limited in their rate of information transmission they are of value for a
number of reasons. First, there are instances in which a rapid rate of
transmission is of no advantage. For example, in the case of an altimeter,
there is one target, the earth. Its general direction is known and fresh
information as to its distance is hardly needed more than a few times a
second. Observation 100 times a second is actually employed in radar
altimeters, to make possible the reduction of certain errors by averaging,
but even so the rate of information transmission is small.

Second, there are the situations in which, though a little information
may be obtained with ease, a lot is impossible to obtain. Such a situation
arises in the presence of very severe clutter, where pulse systems, even
with MTI equipment, may fail to give any information. Certain doppler
systems, on the other hand, will provide useful and even adequate
information.

Third, the price of rapid transmission of data is a certain degree of
apparatus complexity. In some cases, the gain is not worth the price
and the simpler c-w system is adequate.

Finally, there are some things which pulse-type systems simply
cannot do—work down to zero range, for example.

In the descriptions of c-w systems to follow, they will be presented
roughly in the order of their complexity as to objects, conception, and
apparatus. Most of the systems described have seen some use, although
a few that are included have been tried only briefly.

SPECIFIC SYSTEMS

6- 6. Simple Doppler System. —We describe first a system capable of
detecting one or more moving objects in the presence of large amounts of
ground clutter. In detail, the specifications called for the detection of an
airplane 50 ft above the ground at 10 miles range and aircraft at higher
altitudes at 15 miles range. Also, the system later proved most useful
for measuring velocities of projectiles.

It will be observed that, in principle, the simple device shown in
Fig. 51 can do all that is required. Practically, however, two important
modifications must be made.

First, steps must be taken to keep as much transmitter power as
possible out of the rectifier. There are two reasons for this: (1) the
only practical rectifiers at microwave frequencies are crystal detectors
and these would burn out if connected, as in Fig. 51, to even a low-power
transmitter; (2) if the rectifier did survive, it would respond to amplitude
modulation of the transmitter and, since it can be found from Eq, (2 4a)

Sec. 5-6]

SIMPLE DOPPLER SYSTEM

133

that the returned signal will be 10“ 7 or 10~ 8 times the transmitted signal
in voltage, it follows that amplitude modulation of the transmitter
would have to be held below this value in order not to be obtrusive.
Though perhaps not impossible this would certainly be difficult.

The easiest way to keep transmitter power out of the receiver is to
use separate transmitting and receiving antennas, and this was the course
adopted. With a moderate amount of work on the antennas, the leakage
from transmitter to receiver can be made to be of the order 10 _s or less
in power. Another power of 10 is canceled by an adjustable leakage
path from transmitter to receiver. Further than this it does not pay to
go since reflection from nearby ground objects contributes a leakage of
this same order.

It has often been suggested that a single antenna would be satis¬
factory if a bridge-like system were used similar to that used in two-way
telephone repeaters. Ordinarily however the single antenna is not
satisfactory., For one thing, the increased antenna gain resulting from
greater available dish area is lost because of the power used by the
“artificial” antenna which balances the real one. More important, since
very slight mechanical changes will spoil a 60-db balance between two
equal voltages, such bridge systems tend to be highly microphonic.

The second modification relates to the intermediate frequency of the
crystal mixer. The reader will have observed that the system is well
described as a superheterodyne with zero intermediate frequency, the
leakage from the transmitter constituting the local oscillator power and
the modulation frequency being the doppler frequency. The only
unconventional feature is that the signal is single sideband. 1 Of course,
the absolute sensitivity limit of such a system depends on kT and the
bandwidth of the amplifier. Experimentally, however, this limit is not
even remotely approached because a crystal detector, when passing
current, generates a noise analogous to carbon microphone hiss. This
noise increases with decreasing frequency and is enormous compared
to thermal noise for audio frequencies. To avoid this excess noise a
local oscillator is introduced and amplification done at some normal
intermediate frequency, 30 Mc/sec for example. At this frequency the
excess noise is negligible. In the i-f amplifier a strong component is
found due to the beat between leakage from the transmitter and power
from the local oscillator, and a much weaker component, due to the
target, displaced by the doppler frequency. After suitable amplification
these two frequencies are passed into a second detector whose output
signal consists of a d-c component associated with leakage from the

1 It is not difficult to make systems that determine on which side of the carrier the
sideband lies, and are thus able to discriminate between approaching and receding
targets.

134

C-W RADAR SYSTEMS

[Sec. 5-6

transmitter, and the doppler frequency. The d-c component is removed
by passage through a transformer, or otherwise, and the doppler frequency
is used to actuate the indicator.

An incidental but important advantage of this modification is that
it enables the use of a suitable and easily adjustable crystal current.

These modifications are introduced in a manner indicated in Fig. 5-5
which shows a block diagram of the system. Everything is straight¬
forward, except for the local-oscillator power which is obtained by
modulating the transmitter and selecting a suitable sideband by means
of a bandpass filter. This insures a constant intermediate frequency and
avoids any tuning problems. Frequency-doubling is employed in the
modulator to avoid difficulties in keeping leakage from the crystal
oscillator out of the i-f amplifier.

Fig. 5-5.—Block diagram of simple doppler-type radar system.

Design Procedure .—Having blocked out a proposed system, we may
now sketch the design procedure that fixed the various apparatus con¬
stants and dimensions.

Design commenced with the choice of an indicator. A voltmeter
will certainly work, but experience has shown that a speaker or pair of
earphones, in conjunction with the operator’s hearing sense, is much
more effective provided the frequencies to be detected lie in the range
between a few hundred and a few thousand cycles per second. 1 Within
this range, the ear easily recognizes pure tones in the presence of hiss
even when the pure note is much too weak to be seen on an oscillograph.
This phenomenon is analogous to the averaging performed by the eye
when looking at an A-scope, as discussed in Chap. 2. Rough experi¬
ments show that the ear will detect a pure tone in the presence of hiss
when the tone is stronger than the noise in a 200-cps bandwidth. If
the ear can do this over the range 200 to 3000 cps, then by using the

1 A detailed study of the aural detection problem can be found in RRL Report
No. 411-86, May 5, 1944.

Sec. 5-61

SIMPLE DOPPLER SYSTEM

135

simplest possible indication method, a power gain of roughly 15 to 1 over
what might be had by using voltmeter or oscillograph can be achieved.
Aural indication is therefore the logical choice.

This decision, together with the maximum target speed, almost
determines the wavelength, for the doppler frequency must be chosen
to lie in a range for which the ear is sensitive. Thus X = 10 cm gives,
by Eq. (1), 8.9 cps/mph or about 3000 cycles for 300 mph. At the time
this system was designed, faster planes were not common. Even so,
a somewhat longer wavelength might have been desirable, but 10 cm was
chosen because good tubes were available at this wavelength.

This wavelength proved satisfactory, but it sometimes gives doppler
frequencies rather below the frequency region in which the ear is sensitive.
To overcome this difficulty, provision was made to modulate the audio
signal with a 500-cps tone. The modulator was a balanced one, so that
the 500-cps carrier output-was zero when the signal was zero. The result¬
ing variations in amplitude of the tone were quite distinctive, even in the
presence of the noise modulation, and carried the effectiveness of the
system down to frequencies as low as desired.

The wavelength being determined, the antenna size was chosen.
To get as much range as possible, this was taken as large as was feasible
without either (a) making the device impractically large or (b) getting
the beam so sharp that at the specified angular rate of scan the beam
would be on the target too short a time for the listener to hear it. Both
requirements led to a diameter in the neighborhood of 40 in., the value
finally chosen.

It now remained only to estimate the power required. This could
be done either on the basis of experience with similar systems or by
calculations of the sort outlined in Chap. 2. As a result of such considera¬
tions, a power of 10 to 15 watts was chosen.

This completes the discussion of the basic design of the system. A
few of the apparatus details will be given later but first various points
will be discussed which are not mentioned in Chap. 2 but which are of
importance in computing the range. These all relate to the effective
bandwidth, the geometrical factors that determine the transmission
attenuation being the same for pulse and c-w systems.

Effective Bandwidth .—What then, in principle, determines the mini¬
mum bandwidth of a doppler system?

If we use a simple indicator, such as a voltmeter, the bandwidth
must be sufficient to include the doppler frequencies of all targets of
interest. This bandwidth is then determined simply by the wavelength
and the range of target velocities.

If, however, we consider only targets of one radial velocity, or use
some more complex indicator that divides the possible doppler range

136

C-W RADAR SYSTEMS

[Sec. 5-6

into small bands and looks at each band separately, there are certain
limits that determine how small the band may be—limits other than the
obvious one of the response time of the indicator. Three such limits
are discussed in the following paragraphs.

The first is due to the modulation arising from scanning. If the
system is scanned, the beam will be on the target for only a finite time,
with the result that even a single-frequency doppler signal will be spread
over a band whose extent will be roughly the reciprocal of the time
during which the beam is on the target. This is obvious enough, and
would not be worth further discussion, were it not for the fact that the
same consideration arises in connection with the system’s ability to
reject clutter. The presence of scattering objects on the ground gives
rise, as we have seen, to a d-c component in the output signal of the
second detector. This direct-current component will be a function of
azimuth angle and so, as the system scans, we find at the second detector
output “varying direct current”—that is, direct current plus various
low-frequency components extending up to a maximum frequency
roughly given by the reciprocal of the time the beam is on the target.
But the ground returns are so enormous compared to target signals that
one might fear that even the tails of the ground-return frequency spec¬
trum would be large compared with the desired signals. Actually, this
fear is not realized, as will be shown by a brief calculation.

The general idea on which this calculation is based is as follows:
If the system scans at a uniform rate, the system output signal as a
function of time as it scans across a fixed target depends on the directivity
as a function of angle. The frequency spectrum is then the Fourier
transform of the directivity function. But this directivity depends
on the illumination of the dish and is in fact the Fourier transform of the
illumination as a function of distance across the dish. But the Fourier
transform of a Fourier transform is the function itself, and so we find the
interesting theorem that the frequency spectrum due to scanning has the
same form as the function representing the illumination of the dish.
Actually, the above statement represents a slight oversimplification
because we have assumed that the antenna directivity enters only once
whereas actually it enters twice, once in the sending process and once
in the receiving. Taking this into account and carrying out the cal¬
culation, we find that the spectrum due to scanning, which we shall
call g{ o>), is given by

g(u>) ~ [ E(y)E(u - y) dy,

with

, de

y = kx Tt’

( 3 )

Sec. 5-6]

SIMPLE DOPPLER SYSTEM

137

where E(x ) is the dish illumination as a function of x, the transverse
distance from the axis of rotation; k = 2x/X; and dd/dt is the angular
rate of rotation. Now E is zero outside the range x = ± d/2 for a dish

with diameter d and so g(oi) is zero for kd ^ < u. This corresponds,

incidentally, to the doppler frequency associated with the motion of the
edge of the dish or, what is usually about the same thing, the number of
beamwidths scanned per second. Although this calculation is more
complicated for separate transmitter and receiver dishes, etc., the
important general conclusion stands—namely that, in so far as the
approximations used are good, the spectrum produced by scanning is
definitely confined to a finite frequency range.

Another lower limit on bandwidth is set by the modulation due to
fluctuation in target cross sections. If the target is an airplane, for
example, inspection of Fig. 3-8 shows that even moderate yawing will
introduce large fluctuations in returned signal. The frequency spread
so introduced depends on the rate of yaw and on the ratio of the target
dimensions to the wavelength, this ratio determining the number of
pattern lobes per radian. Calculations are difficult because of lack of
data, but experimentally a value of about 30 cps at X = 10 cm is found.
Another and equivalent point of view is that when the plane is turning
different parts have different doppler frequencies.

Finally there is, in principle, a limit set by target acceleration.
Thus if we have an accelerating target it may happen that the doppler
frequency will transit the pass range of the band-determining filter
before the filter has time to build up, in which case the signal may be
missed. If the acceleration is a, and the band is Ar, so that we require a
buildup time of 1/Ar, we then find

Ar >

(4)

with a in ft/sec 2 .and X in cm.

Apparatus Considerations .—Having blocked out the system and
determined the leading design constants, we can now proceed with the
detailed engineering. Figures 5-6 and 5-7 show the final result; there
follow a few remarks as to the more important ways in which the engineer¬
ing technique for this system differs from that used in pulse systems.

There are no high pulse powers and both intermediate- and audio¬
frequency amplifiers are narrow-band. Gains per stage are limited by
stability rather than by bandwidth; in other words, the technique is
like that of ordinary radio rather than like that of television. Because
of the large size of the leakage signal relative to the target signal, only

C-W RADAR SYSTEMS

138

[Sec. 5-6

relatively small i-f amplifications can be used, the remaining amplification
being done after the second detector.

The most important consideration in doppler work is keeping the
transmitter frequency modulation down. This will be discussed in

Receiving

paraboloid

Transmitter receiver unit

paraboloid

Jack screws

Elevation scale

Elevation

handwheel

scale

shaft and
drive motor assembly

Horizontal shaft
and yoke

handwheel

T ig. 5-6.—Rear view of 10-cm doppler system. (Courtesy of Sperry Gyroscope Company,

Inc.)

detail in connection with another system but it should be noted here
that short-time frequency stabilities of the order of a part in 10 10 must
be attained if the system is to work with full sensitivity in the presence
of ground clutter. This requires careful attention to microphonics and
to power-supply filtering. Also, the transmitter filament must be sup-

Sec. 5-7]

RANGE-MEASURING DOPPLER SYSTEM

139

plied with direct current or conceivably with alternating current of
frequency above the pass frequency of the audio amplifier.

6-7. Range-measuring Doppler System. —In order to measure the
range of one or more targets, the outgoing wave must be marked, or
modulated, in some way and the time required for the marks on the
wave train to return must be measured. The modulation may be of
either the amplitude or the frequency type, the techniques for the two
methods being quite different.

The most familiar method for measurement involving amplitude
modulation is to emit a pulse of waves and determine the time delay in

M amplifier
chassis

Crystal mixer
t-f mixer

modulator
Deal oscillator fitter

Blower motor

Transmitter output cable
Local oscillator cable

reflector

Audio amplifier and
translator chassis

Temperature control vane
Filter mixer

To power supplies
and control box

Fig. 5-7.—Transmitter-receiver chassis of 10-cm doppler system. (Courtesy of Sperry
Gyroscope Company, Inc.)

the arrival of the reflected pulse. This modulation gives rise to a large
number of sidebands, and the distance of the target may be regarded
as determining the relative phase shifts of the various sidebands on their
return path.

The fundamental point here is the determination of the relative phase
shifts, not the multiplicity of sidebands. Actually only two frequencies
are needed, as we will now show by considering the simplest possible
amplitude-modulated c-w system capable of measuring range.

The system consists, in principle, of two separate systems like that
just described, the two systems having transmitter frequencies differing
by an amount f r . The transmitted and received spectra then appear
as in Fig. 5-8 with the tw T o receivers receiving / 0 and / 0 + / r by leakage

140

C-W RADAR SYSTEMS

[Sfc o-7

and fo ± Jd, fo + fr ± fo', from the target, with f D and f D ’ very slightly
different because of the difference in transmitter frequencies. This
slight difference in doppler frequencies leads to a phase difference between
the two doppler-frequency outputs which is a linear function of time,
just as the target range is a linear function of time for constant radial
velocity. This suggests that the phase difference is a measure of the

range.

This is in fact the case, as may be shown analytically, or qualitatively
by the following argument. If the target is very close to the system,
~ the number of wavelengths from trans-

| mitter to target and back will be the

1 1 same, even though the two transmitter

£ = wavelengths differ slightly. Thus the

| I leakage and target signals will be in

| phase or out of phase at the two re-

^ -—- ceivers simultaneously and the doppler

/„ f 0 + / r outputs will be in phase for this range.

As the target gets further away, this
| phase difference increases, finally be¬
ll coming 2t when the number of wave-

81 lengths to the target and back is one

| E greater for / 0 + J, than for ft,. Ana-

S I lytically one easily finds that the

-LL-il-_ range is given by

Fig. 5-8. —The upper figure shows
the frequencies present in the trans¬
mitter spectrum. The lower gives the
same information for the receiver. with <t> the phase shift between the two
Frequencies fo and fo + f T in the receiver , , c

are due to leakage from the transmitter; doppler lreqU6ncieS.
the same frequencies ±/o come from the This is a perfectly feasible system

target ' and has worked in the field. It is

not nearly so complicated as appears from the description since the two
transmitters can be combined, as also can most parts of the receivers.
The apparatus is essentially like that of the system described in Sec. 5-6
with the addition of a modulator for the transmitter, another audio
channel, and a phase meter. No detailed description will be given
because, as yet, no great practical application of the method has been
made. The principal difficulty at present is the lack of a well-developed
phase meter that will work over a range of both frequency and amplitude.

Nevertheless, some further discussion is in order both because of the
principles involved and because some future use may be made of the
idea.

Four points of principle should be noted. First, to measure the

1 c

r -H J*

Sue 5-7J

RANGE-MEASURING DOPPLER SYSTEM

141

distance to a single target, only one additional sideband is needed.
Second, the presence of the doppler shift, applying as it does to both side¬
bands, does not interfere with distance measurement. Third, the two
receivers are separate and their bandwidths are determined by the
doppler frequency, not by the modulation or repetition frequency.
Fourth, we now have two design frequencies, f d and /,, and it is a matter
of great importance which is the greater. If / D «/ r , as the diagram
above implies, the apparatus works as described. If f, < f,>, the opera¬
tion is the same in principle but the beat f r between the two leakage
signals will be within the doppler band and unless special measures are
taken this beat will completely
dominate the target signals.

Since the sense of this ine¬
quality is an important factor in
all the systems to be described
from here on, this section closes
with a few further remarks con¬
cerning it.

The doppler frequency is, by
Eq. (1), dependent only on the
wavelength and the radial velocity.

Values as a function of wavelength
and for various speeds are given
in the curves of Fig. 5-9.

The modulation frequency is
ordinarily made as large as pos¬
sible, in order to get the maximum possible change of phase with change of
range. The limit is reached when, at extreme range, the phase shift
is 2 w radians; ranges beyond this are ambiguous. This condition leads
to the inequality

6 8 10 20 40 6080100

X in cm

Fig. 5-9.—Doppler frequency as a function of
wavelength, for various radial velocities.

fr ^

2r„

(6)

a result that is entirely analogous to the similar relation discussed in
Chap. 4. A plot of Eq. (6) using the equality sign is given in Fig. 5T0.

Inspection of the last two figures will show that, for radar systems
in general, there is no “usual” case. One may perfectly well have either
sign of the inequality. For example with X = 3.3 cm and velocities
greater than 100 mph, f D is greater than 2950 cps and a maximum range
of 93 miles w'ould give/, :£ 1000 cps. On the other hand a lower velocity
and shorter range might, in conjunction with a longer wavelength, lead to
numbers like v T = 10 mph, X = 10 cm, r = 9.3 miles, values which would
give fo = 89.4 cps, f r ^ 10,000 cps.

142

C-ll' RADAR SYSTEMS

[Sec. 5-7

When J T < fo, the system as outlined must be modified by placing
infinite-attenuation filters after the second detector. The filters are
designed to remove f r completely, while leaving all but closely adjacent
frequencies undisturbed. In principle, this is no different from the
infinite-attenuation filters already present to remove the d-c signals due
to clutter. Practically, somewhat more trouble is involved, since zero
frequency filters are stable because neither the frequency nor the filter
tuning can change, while both possibilities are present for frequencies
other than zero. Usually also, either by accident or design, various
harmonics of /, will be present and these also must be filtered out.

This is the first case we have encountered of a general and almost
exact 1 theorem to the effect that any periodic modulation can produce

10 20 40 60 100 200 400 1000

r max in miles

Fig. 5-10.—Maximum repetition or modulation frequency as a function of maximum

unambiguous range.

in the receiver, whether by direct leakage or reflection from stationary
objects, only output signals that have the same periodicity; these output
signals can therefore be removed by a sequence of infinite-attenuation
filters tuned to frequency zero and to all harmonics of the modulation
frequency.

Finally, we note that this system will handle only one target. If
more are present the precise behavior depends on the type of phase
meter used and the best that can be done is to choose a type that meas¬
ures range to that target which gives the most intense reflection.

If the system is required to handle more than one target at a time,
discrimination may be made either on the basis of range or of doppler
frequency. If range is used, more sidebands are called for, and the

1 The theorem would be exact if the carrier frequency were an integral multiple
of the modulation frequency. When this is not so, the deviations are of the order
fr/fo or less and are usually negligible.

Sec. 5-8]

F-M RANGE-MEASURING SYSTEM

143

number of range intervals that can be distinguished is essentially the
same as the number of sidebands added. A system of this type will
be described later. If discrimination of targets is to be made by doppler
frequency, the various doppler tones can be separated with filters.

The more sidebands used, the more information is obtained per
second because of the wider band. In discriminating by frequency,
either duplicate audio systems may be used to increase the information
flow, or a sweeper of some sort may be used—with resulting loss of speed.

6-8. F-m Range-measuring System. —The next system to be
described is one that illustrates the f-m technique of range measurement.
The specific problem is that of a radio altimeter. In this case, we wish
to measure the distance to a single target, no clutter is present, and the
target radial velocity may be zero. Also, the system must w r ork down
to zero range. The system described below' w'as very successful and

Fig. 5*11.—Simplified block diagram of f-m system for measuring range.

it and the proximity fuze are the tw'O c-w r systems that have been most
widely used.

The general method may be explained by the block diagram of
Fig. 511 and the graphs of Fig. 5T2. Here the transmitter emits waves
of a frequency 1 that varies linearly with time, oscillating above and below'
the mean frequency fa, as shown in Fig. 5-12. These waves arrive at the
receiver both by a direct connection and by reflection from the target.
Since the trip to the target and return takes time, the received frequency
curve, indicated by the dotted line, is displaced along the time axis
relative to the transmitted frequency. Also there might be a displace¬
ment along the frequency axis due to doppler effect. This w r e disregard
for the moment. The two frequencies, when combined in the mixer,

1 We note that two types of “frequency analysis” are useful in analyzing this and
other systems. One is the Fourier method, in which some curve is decomposed into
a sum of sine waves, each of constant amplitude and frequency and extending in time
from — oo to T so. According to the other method, frequently useful in discussing
f-m systems, we say that any function of time can be represented by a function of the
form a cos ui where a and u are functions of t and are so chosen as to get the best fit
at any value of l. In cases where the latter procedure is useful, a and u are slow
functions of (.

144

C-W RADAR SYSTEMS

[Sec. 5-8

give rise to a beat 1 /„, as shown in the bottom graph of Fig. 512. Plainly
enough, the greater the target distance, the greater this beat frequency;
its magnitude is then a direct measure of the range. The signal of this
frequency is therefore amplified and limited, and the frequency measured,
usually by a cycle-counting device of some sort. The frequency meter
is then calibrated in terms of range.

Such a system would work, as described, and would also work on
multiple targets. But linear frequency modulation is not easy, and
for single targets the operation is not greatly affected by a change from
linear to sinusoidal frequency modulation. The difference frequency
then varies sinusoidally with time,
but the important point remains,
namely that the mean magnitude
of the difference frequency de¬
pends on the range. Sinusoidal
frequency modulation is therefore
adopted since it requires simpler
apparatus and accomplishes the
same result.

There is one subtlety that is
worth some discussion. If the
mean or carrier frequency were an
integral multiple of the modulator
frequency, it is obvious that the
output of the mixer would be
periodic with periodicity corre¬
sponding to the modulating fre¬
quency. This would mean that
each modulation period would contain the same number of cycles.
This number is then integral and we see that the frequency meter can
read only 1, 2, • • • , n times the modulating frequency. Actually,
the same conclusion holds even with no special relation between modula¬
tion and carrier frequencies, if, as is usual, we use a cycle-counting type
of frequency meter. Naturally, it is of interest to translate this step¬
wise behavior of the frequency meter into altitude readings. For the
linear-modulation case we easily find f a = Af r Afh/c with f, the modu¬
lating frequency, A/ the total frequency swing, /„ the beat frequency,
and h the height. Solving for the height and introducing the fact that
f a is quantized in steps of f,, we find for the error oh

1 It is beats of this sort, which may be described as due to time-delay demodulation
of FM, that are regarded as spurious signals in the system described in Sec. 5-6 and
that must be avoided by reducing FM of the transmitter to the lowest possible
value

Fig 5-12. —The upper figure shows, in
the full line curve, the instantaneous trans¬
mitter frequency as a function of time. The
dotted curve is the received frequency. The
lower figure shows the difference, or beat,
between transmitted and received fre¬
quencies, as a function of time. The hori¬
zontal axis in the upper figure corresponds to
the mean transmitter frequency/c.

Sec. 5-8]

F-M RANGE-MEASURING SYSTEM

145

(7)

This is of the nature of a maximum error and can be much reduced
by averaging over a number of modulation cycles.

Design Procedure .—Design of such an altimeter is begun by using
the above equation, together with an allowable altitude error, to pick a
suitable A/. In the present case A/ was chosen as 40 Me/sec, which
corresponds to Sh = 6 ft, and so, because of averaging, to a rather smaller
operational error.

The mean transmitter frequency is now chosen. This must be
fairly high in order to keep, the frequency variation from being an impos¬
sibly large fraction of the mean trequency. On the other hand there is no
gain in very high frequencies and there may be some loss in intensity
over such terrain as forests. These considerations, plus a consideration
of the tubes available, led to the choice of a mean frequency of 440
Mc/sec, which can be obtained from acorn tubes; the frequency modu¬
lation is accomplished mechanically.

The modulation frequency is next chosen to give a convenient range
of beat frequencies/„, subject to the restriction that the time of a modulat¬
ing cycle shall be long compared to the maximum signal transit time.
A value of 120 cps was picked. This gives f a = 8000 cps at an altitude of
400 ft. A second range of 0 to 4000 ft is obtained by reducing A/ to
4 Mc/sec.

This completes the major specifications, except for the power. Prac¬
tically speaking, power must be decided on the basis of experience,
calculations of available power and thermal noise power being quite
useless since, in practice, the limitation is not thermal noise but micro-
phonics, etc. Thus if we consider the earth as a diffuse reflector we
easily find the received power is (l/27r)(A/r 2 ) times the earth’s reflection
coefficient and times the transmitted power. Even for very small
transmitter powers and reflection coefficients, this power is large compared
to thermal noise. On the basis of experience, then, it was decided that
the 0.3 watt available from an acorn tube would be sufficient for altitudes
up to 5000 ft, provided certain points of apparatus detail were correct,
as explained below.

Apparatus Considerations .—The leading parameters having been
specified, one can proceed with the detailed design. This is straight¬
forward, except for certain steps necessary to reduce various spurious
signals in the receiver which might limit the range.

These signals, for the most part, are due to amplitude modulation in
the transmitter. This amplitude modulation comes from microphonics
and from slight variation of transmitter amplitude with frequency.

146

C-W RADAR SYSTEMS

[Sec. 5-8

Modulation from the latter source is at the modulating frequency and
low harmonics thereof. These spurious signals may be greatly reduced
by two devices. First, one makes the mixer of Fig. 5T1 a balanced one

Fig. 5-13.—The AN/APN-1 frequency-modulated radar altimeter. (Reprinted from
Electronics.)

(see Vol. 24) with the result that, if the balance is good, amplitude
modulation from the transmitter balances out in the detector output.
Second, the amplifier that precedes the limiter is given a response that is
a rising function of frequency. The spurious signals, being largely of

Sec. 5-9] MULTIPLE-TARGET F-M RANGE MEASUREMENT

147

frequency lower than the desired signals, are thus discriminated against.
Roughly speaking, the response should rise linearly with frequency, since,
on a voltage basis, the incoming signals go down at about this rate in
range and thus in the equivalent frequency. This frequency distortion
serves a second purpose in that it makes the output signal less dependent
on altitude so that the limiter does not have to work over such a large
range of amplitude. The complete device is illustrated in Fig. 5-13.

The effect of doppler shift is to raise or lower the dotted curve (Fig.
5-12) corresponding to the returned signal. With the proportions here
used and with the aircraft in reasonably level flight, the doppler frequency
is almost always less than the beat frequency due to altitude; con¬
sequently the end result is that there are somewhat fewer cycles of beat
frequency in one half of the modulating cycle, and somewhat more in
the other, the total number per cycle remaining the same. The difference
in numbers of cycles in the two halves of the modulation period is then
a measure of the doppler frequency. This difference can be measured
in various ways, and has been used, along with the altitude information,
in various developments of the device here described.

6-9. Multiple-Target F-m Range Measurement. —In the absence of
clutter and doppler shift almost the same methods can be used with a
plurality of targets as with a single target. In this case linear frequency
variation with time is almost essential, and the triangular form of Fig.
5-12 is probably most convenient, though a saw-tooth variation might
be used. The detector output then contains a number of frequencies,
one corresponding to each target range present. Preferably these fre¬
quencies are detected by some device such as a Frahm vibrating-reed
frequency meter, which indicates all frequencies simultaneously. If,
however, time is no object, a device that scans the frequency range may
be used. A variable frequency can be added to the signal frequency and
observations made when the sum frequency falls in the pass band of a
resonant circuit. Variants of this idea sweep either / r or A/ and observe
when the target frequency falls in the pass band of a resonant circuit.

Any of these scanning devices greatly increases the time required to
obtain the desired information. Thus if we have a frequency band /
which is to be split into n pieces, the time required for such a device as a
Frahm meter to respond is of the order n/f, whereas if the n frequency
intervals are observed in sequence the time is n-/f.

The general design procedure is essentially the same as that described
in Sec. 5-8. First we decide on the allowable range error Sr and determine
from this the total frequency swing A/ by means of Eq. (7):

C-TT RADAR SYSTEMS

148

[Sec. 5-9

We may note that 1/4A/ is analogous to the pulse time; it determines
the width of waveband transmitted and the range accuracy.

Next, one determines the modulation or repetition frequency f T .
As in pulse systems, this depends on the maximum range. But whereas
in pulse systems f r may actually be as much as c/2r, in the present systems
one must have f r markedly less than c/2r in order that not too large a
fraction of the time will be wasted while the sign of the beat frequency is
changing. Subject to this upper limit, the choice of f r is determined by
considerations of bandwidth, response time, and apparatus convenience.
The smaller f r , the narrower the band and the slower the response.
Also, the beat frequency, which varies with f r , should be kept in a range
suitable for the frequency meter to be used.

The maximum beat frequency is then determined as 4/ r A/(r/c), and
an indicator working up to this frequency by steps of f, is designed. The
number of steps is thus about r/Sr.

This method of ranging, like the pulse method, makes no special
requirements on the carrier frequency, which is then chosen on the basis of
other considerations.

The power required depends on the usual things, including the band¬
width, which in this case is the bandwidth of one element of the fre¬
quency meter- which should be about / r .

This scheme, although it has not been highly developed, will undoubt¬
edly work much as described. High range accuracy and small band-
widths are possible—in fact one may have both at once. Thus one
might have a repetition rate, and so a noise bandwidth, of, for example,
10 cps while having a frequency swing of 40 Ale sec, which would give
range accuracy corresponding roughly to a tj-mscc pulse. And this
latter would be achieved without a wideband i-f or video.

If, however, we attempt to modify the system so as to allow the
presence of clutter, and therefore also a doppler shift of the signal coming
from the target, two difficulties arise.

First, although the clutter may, in principle, be eliminated by infinite
attenuation filters tuned to the repetition frequency and multiples
thereof, the number of filters required is of the order of r Sr, and if this
number is large the system may be impractical. This limitation appears
to be fundamental and arises in similar form in all other systems. But
even if we neglect the multiplicity of the filters, there is considerable
doubt whether practical means of frequency modulation can be devised
that will make successive modulation cycles as nearly identical as is
needed for filtering out really serious clutter.

Second, as a result of the doppler shift, each target gives two output
frequencies, and so two range indications. The seriousness of this
depends on the ratio of the doppler frequency to mean beat frequency.

Sec, 5 10]

ALTERNATIVE F-M RANGING SYSTEM

149

This ratio depends on target speed, wavelength, repetition rate, and
range accuracy, and might conceivably have almost any value. But in
many cases the value will be too large for this system to be useful.
Specifically, the maximum beat frequency may be written as f r (r/Sr) so
that, for example, 1 per cent range accuracy and /, = 10 cps gives
f a = 1000 cps, which may be compared with a doppler frequency of
894 cps for 10 cm and 100 mph.

6-10. Alternative F-m Ranging System. —Another scheme of the
f-m type which is designed to work on multiple targets and in the presence
of clutter may be understood by reference to Fig. 5-14. This shows, in
the full curve, a sinusoidal depend¬
ence of the transmitted frequency
on time. The total frequency
swing is made large compared to
the doppler frequency. The re¬
ceived frequency, indicated by the
dotted line, is a similar curve but
(a) displaced to the right by time
delay resulting from transmission
to the target and back and ( b ) dis¬
placed vertically by doppler shift.

If now the difference between the
transmitted and received frequen¬
cies is passed through a low-pass
filter whose pass band includes fre¬
quencies as high as the maximum
doppler frequency, there will, in
general, be little signal output be¬
cause the difference frequency will
be greater than the doppler fre¬
quency over the majority of the
modulation cycle. If, however, the modulation frequency is adjusted
so that one cycle corresponds to the transmission delay time, the differ¬
ence frequency will always just equal the doppler frequency and so a
large output signal will result. Thus, as the modulation frequency is
varied, output occurs whenever n/f r = 2r/c with n any integer and r
the distance to a target. Ground clutter, having no doppler shift,
gives an output that is periodic with period corresponding to the modula¬
tion frequency. The d-c component is easily removed and, if fo < f r ,
the other components are removed by the low-pass filter, which passes
only up to / D , If, therefore, f D < f T ground clutter may, in principle,
be removed.

A variant of this scheme turns the receiver off during one modulation

Fig. 5-14. —The full curve in the upper
graph shows the instantaneous transmitter
frequency as a function of time; the dotted
curve shows the received signal; and the
dashed curve, the beat between the two.
The lower curve shows the same quantities
when 2 r/c = nf T , in which case the beat
frequency is constant at the doppler value.

150

C-W RADAR SYSTEMS

[Sec. 5-11

cycle, and turns the transmitter off and the receiver on during the follow¬
ing cycle. This permits the use of a single antenna and also reduces
the clutter intensity by making it possible to gate out the strong returns
from near-by objects.

Difficulties with systems of this type are as follows: (1) determination
of range by variation of f r takes much more time than is justified by the
receiver bandwidth; (2) the distance measurement is unambiguous
only over a 2-to-l range; (3) proportions must be such that/ D < ft —this
means long wavelengths and/or slow targets; (4) it is difficult to get the
modulation cycles to repeat well enough for suppression of really serious
clutter.

6-11. Pulse-modulated Doppler System. —The last system to be-
described works against the heaviest ground clutter, and, in principle,
on a plurality of targets and with no restriction on the relative values
of doppler and recurrence frequencies. Practically, there are limits
on the last two factors, the limits being set by questions of apparatus
complexity.

A block diagram is shown in Fig. 5-15 and the operation may be
described as follows. If, as we shall assume for purposes of explanation,
only a single target is to be observed, the transmitter is turned on for
half the keying cycle and off during the other half by means of the
modulator, square-wave generator, TR and ATR tubes. If a mul¬
tiplicity of targets must be handled, the transmitter pulse is made
correspondingly shorter. The transmitter power then follows the Curve
a of Fig. 5T6, and the receiver input follows Curve b with the time delay
depending on the range and with the dotted part of the received signal
rejected because the receiver is off. 1 This received signal is amplified
by a conventional superheterodyne receiver whose only special feature
is the derivation of the local-oscillator frequency from the transmitter
frequency by the addition of 30 Mc/sec. This 30 Mc/sec is then sub¬
tracted in a second detector so that the received signal is translated
down to zero frequency.

Consider the voltage at point 1 in Fig. 515 just after the second
detector. If the returns are from a stationary target the voltage is of
the form shown in Graph a of Fig. 5-17. This voltage is periodic and
has magnitude depending on the target cross section and on the exact
phase of the returned signal—a change of range of X/4 resulting in a
reversal of sign. If the target moves, the change of range causes a
periodic oscillation of amplitude, the resulting signal being like that of
Graph b Fig. 5-17 and having an envelope which is a sine wave of
doppler frequency.

1 Actually, the receiver gate is not opened until several microseconds after the
transmitter is off. In this way ground clutter due to nearby objects is eliminated.

Fio. 5-15.—Block diagram of pulse-modulated doppler system.

Sec. 511 ] PULSE-MODULATED DOPPLER SYSTEM

152

C-W RADAR SYSTEMS

[Sec. 5-11

Now the Fourier resolution of Curve a wall contain the repetition
frequency and multiples thereof, whereas Curve b contains f D ± nf r
but no multiples of f r (unless ft, is a multiple of f r ). Thus the first or
“clutter” filter that attenuates f r and multiples thereof, while leaving all
rise, will remove all signals due to stationary objects, while leaving those

due to moving objects undisturbed. At
point 2 in Fig. 5-15, therefore, the signals
are like those of Fig. 5175, and do not
contain the frequency /,.

The signals are now passed through
a full-wave rectifier, the voltage at Point
3 in Fig. 5T5 being like Fig. 517c.
This curve now contains harmonics
nfr ± mf D .

The various doppler sidebands and most of the noise are now removed
by passage through a filter that passes only f, and its multiples, whereupon
the voltage at Point 4 has a form like that shown in Fig. 5-17d. Thus
the clutter, the doppler frequency, and much noise have been removed,
while the position of the trailing edge
of the pulse, which is a measure of
the range, is undisturbed.

The time delay of the trailing
edge of the wave at d, relative to the
modulating pulse, is now a measure
of target range. This time, or range,
may be displayed on the linear radial
sweep of a PPI tube by differentiat¬
ing the voltage and using the result
to intensity-modulate the beam.

A few minor points remain to be
considered. First, the explanation
has assumed that the bandwidth is
large enough to pass square waves
without distortion. Actually, the
operation is substantially the same
when only a few harmonics of / r are
passed. Second, the function of the
attenuated square-wave voltage in¬
troduced after Point 1 is to balance
out the square-wave voltage due to the d-c component of receiver noise,
as modulated by the gating. Finally, it should be noted that the last
filter can have fairly narrow pass bands, thereby considerably reducing
the noise.

(a)

(i)

LJi__rL_jL__rL_

k -n"Tr>

(c)

(d)

n_n_ r_j“l_

Fig. 5-17. —Curve a shows the voltage
at Point 1 (cf. Fig. 5-15) due to a stationary
target and b shows that due to a moving
target; the dotted envelope curve corre¬
sponds to the doppler frequency. Curve
c is the result of passing b through a full-
wave rectifier, and d is the result of
filtering c.

—I [■— 2 r/c

w Jj'n_rn_rn_

Fig. 5-16.—Transmitted and re¬
ceived powers as a function of time.

Sec. 5-11]

PULSE-MODULATED DOPPLER SYSTEM

153

Design Procedure .—The leading requirement in the design of a system
such as that described above was a range of 75 miles on single targets
moving at speeds up to 400 mph, even in the presence of extreme ground
clutter.

First, since ability to deal with multiple targets was not required,
the modulation cycle was taken to be half on and half off. Next, the
repetition frequency was chosen to be as high as possible, consistent
with getting a reasonable fraction of the extreme range signals to return
during the time the receiver is on. Thus the value of f r = 1000 cps,
which was selected, lets the entire return signal into the receiver at
r = 46.5 miles and none at 93 miles, so that at 75 miles about half is
lost. The advantage of a high value of f r is the reduction in number of
stop bands required in the filter.

The dish size and wavelength were chosen—on the basis of range,
propagation factors, and beamwidth—to be 12 ft and 40 cm, respectively.
This latter value also determines the doppler band, which extends from
zero to about 1000 cps for 400-mph targets. Thus we need carry only
one harmonic of the repetition frequency.

The transmitter power depends on geometrical factors in the usual
way, and on the effective bandwidth of the receiver. It might be thought
that this would be the total width of the pass bands in the second filter
of Fig. 5T5, but actually, because of the rectifier between the two filters,
the noise depends on the bandwidths, both before and after this detector.
In fact, the effective bandwidth is the geometric mean of the two band-
widths. The last bandwidth was chosen at about 4 cps, this being the
smallest consistent with the time during which the beam remains on the
target; and the first bandwidth was about twice the maximum doppler
frequency. Thus the effective bandwidth, for noise-computation pur¬
poses, was about 100 cps. With this bandwidth, a transmitter power of
100 watts should give the required range.

Apparatus Considerations .—The leading design parameters having
been chosen, the next subject of discussion is the technical difficulties
involved. There are two chief ones, both having to do with elimination
of ground clutter: (1) frequency, and also amplitude, modulation in the
transmitter must be held to very low values; and (2) the filters, which
reject frequencies 0, /,, 2 f r , etc., present a considerable problem.

As to the first point, the entire operation of the system is predicated
on the assumption that the ground returns are periodic. This assumption
would be completely falsified, if the range of a ground target, measured in
wavelengths, were to change by as little as X/2 in one repetition cycle.
Since, in round numbers, there are 10 6 wavelengths contained in twice the
maximum range, it is apparent that the operation will not even approxi¬
mate the above description unless the short-time frequency stability

154

C-W RADAR SYSTEMS

[Sec. 5-11

exceeds one part in 10®. Actually, much better than this must be done
since the ground returns may be 90 db or thereabouts above the target
returns. Thus, one might expect stabilities of the order of 10 10 to be
needed. Much calculation can be done on this point but, though such
calculation was useful in showing that a workable system was possible,
it will suffice to say here that by very careful attention to detail it was
found possible completely to eliminate all trouble due to frequency
(and amplitude) modulation of the transmitter. The main points were:
crystal control of both transmitter and modulator, very careful regulation
and filtering of power supplies, and operation of important filament
supplies with alternating current (3000 cps) obtained by multiplication
from the repetition frequency.

We next consider the “infinite rejection” filters that are to remove the
ground clutter.

The maximum attenuation required is the quantity of most impor¬
tance. Naturally, this is indefinite since it depends on the terrain, and
pertinent measurements are very scanty. But the attenuation needed
may be estimated in several ways, which agree moderately well, and
finally it was measured on the finished system. Data from all sources
indicate that ground returns in mountainous terrain may be much larger
than is commonly realized—in the present case, of the order of 90 db
above noise.

The first method of estimation is to calculate the largest possible
ground return on the assumption that the return is from a mountain so
large as to fill the beam completely. Such a mountain is certainly
possible, and assuming it to be hemispherical its returns will be larger
than those from a target of cross section cr in the ratio r 2 A/\ 2 o with A
the dish area. In the present case, this comes out at about 110 db.
This is certainly an overestimate because the mountain will generally
not have unity reflection coefficient, and because the part of the model
that does the reflecting—namely, the part of the hemisphere normal to
the line of sight—will usually be missing in actuality. Nevertheless,
the calculation is interesting as indicating that very large ground returns
are possible.

A second estimate can be derived from measurements made at Ellen-
ville, N.Y. with a more or less normal (1-jusec, 100-kw) pulse system.
These measurements showed a ground return 75 db above noise. To
compare these measurements with our present problem, a number of
factors must be taken into account. These are: the difference in pulse
lengths (~ 27 db), the different receiver bandwidths (~ 30 db), and the
different transmitter powers (~ 30 db). Taking these factors into
account, the clutter returns at Point 1, Fig. 5T5, may be very crudely

Sec. 5-11)

PULSE-MODULATED DOPPLER SYSTEM

155

estimated as 100 db above the noise in a 10 3 -cycle band, or 130 db above
that in a 1-cycle band.

A third estimate can be made from measurements on the completed
system at this same location, which showed a clutter 100 db above the
noise in a 1-cycle band. Part of the discrepancy between this and the
above 130-db estimate is no doubt due to crudities in the estimation,
the rest to the fact that the clutter in a 500-Msec pulse will certainly be less
than 500 times that in a 1-^sec pulse because the clutter is not spread
uniformly in range. In any case, whatever the reason, the clutter is
experimentally found to be about 70 db above the noise in the 1000-
cycle audio band, or about 80 db above the noise in the effective band of
100 cycles.

The system, as actually made and tested at this same location, had
92-db attenuation at the “infinite attenuation” points of the filters and
experience showed that this was just comfortably adequate.

From the above results we conclude that the filters must have about
90 db of rejection for satisfactory operation at this particular site.
Measurements at other sites would be valuable in answering the question
as to how representative this site is. Lacking such data, we can only
venture the opinion, based on personal observation, that the location
did not appear unusual in any way—in fact it appears likely that moun¬
tain areas with even higher ground returns may be common.

The width of the rejection bands depends on the variability of the
ground returns. Until now, the ground returns have been assumed
constant, so that the voltage at Point 1 in Fig. 5T5 is actually periodic
and could therefore be removed by filters with infinitesimal bandwidth.
Actually the ground returns vary, with the result that the filter rejection
bands must have a finite width. Using some data of H. Goldstein, 1 a
width of 4 cycles 12 db up from the 92-db bottom of the curve was
chosen. Even if the ground returns had been constant, much the same
bandwidth would have been needed because of modulation due to
scanning. The rest of the curve was-then made as narrow as possible.
This turned out to be about 200 cycles at the 3-db point.

Additional filters for eliminating “window” signals or rain clutter
were also provided and could be switched in when desired. These
filters had much less attenuation than the clutter filters, but the at¬
tenuation extended over a wider frequency range, designed to exclude
doppler frequencies due to motion of “window.”

Although the audio amplifier began to cut off rapidly above 1000 cps,
and the strength of the harmonics of } T decreased fairly rapidly, it was
found necessary to have infinite attenuation filters at 2000 and 3000 cps,

1 See Sec. 6-20, Vol. 13 of this series.

C-W RADAR SYSTEMS

156

[Sec. 511

in addition to those at 0 and 1000 cps. Naturally, these latter filters
were not nearly so critical as the one at 1000 cps.

This concludes the discussion of the design and the leading difficulties
of a system of this type.

Performance was much as expected. In particular, the strong ground
clutter mentioned above was completely eliminated, targets being
tracked regardless of range or position. All other known systems that
have been developed to the field-trial stage were tried at this same site;
none of them eliminated the ground clutter.

The only deficiency of this system, as has been pointed out, is its
inability to function properly when there are a number of targets in the
beam. When this is the case, the range indicated is that of the strongest
target. This difficulty may be reduced as desired by reducing the length
of the transmitted pulse, by correspondingly increasing the number of
filter bands, and so increasing the complexity.

Since the general objects of this system are much the same as those
of the MTI system described in Chap. 16, some comparison is in order,
even though this comparison is difficult and possibly dependent on
personal viewpoint.

First, the two systems regarded from an abstract point of view work
on similar principles. Both have, therefore, much the same fundamental
limitations. Practically, however, the two systems use entirely different
apparatus, and consequently when, as is usually the case, apparatus
limitations dominate, the systems may be expected to be entirely differ¬
ent. Furthermore, because of this apparatus difference, one may expect
future developments to improve the two in different ways and by different
amounts.

Second, the two systems differ in their ability to handle a multiplicity
of targets. As actually constructed, MTI systems use 1- or 2-Msec
pulses and so are capable of handling targets a thousand feet or so apart
in range. On the other hand, the system described in this section works
on only one target, and although a moderate number of additional filters
might be considered as possible whenever anyone wishes to deal with
multiple targets there is certainly a practical limit to their number.
Possibly dividing the total range into 10 pieces would be reasonable.
For traffic control around a busy airport, however, the c-w system would
be almost useless whereas the MTI system would be very good. For
long-range detection of aircraft, an ability tc. handle 10 targets might
well suffice and the c-w system therefore be adequate.

When, on the other hand, one considers severe ground clutter the
system described above has the advantage over the MTI systems. MTI
systems at present reduce the clutter by perhaps 30 db—which in many
locations is adequate. But mountainous terrain that does not appear

Sec. 512)

SUMMARY

157

in any way unusual has been found to have ground clutter 75 db above
noise. Under these conditions, the MTI system would not be expected
to work; the above-described system does work.

6T2. Summary.—In an effort to help the reader who wishes to com¬
pare the various systems described in this chapter, Table 5-1 has been
prepared giving, in tabular form, a summary of the more important
systems of characteristics, both qualitative and quantitative. This
table is worthy of careful study but two limitations must be remembered.
First, the quantities given for numbers of sidebands, noise band, etc.,
are only qualitatively correct; really precise definitions would require so
many qualifications as to render the quantities either useless or confusing.
Second, neither the table nor this chapter pretends to describe all c-w
systems; at least a dozen more are known and no doubt still more could be
invented. It is believed, however, that representatives of all important
types have been included.

From this table, or what has gone before, the reader will perceive
that there have been grouped together, in this chapter, some rather
diverse systems. Perhaps a better, if longer, chapter title would have
been “Systems That Are Not Pulse Systems. ”

If we attempt a classification, the two best starting points appear to
be the questions—does it utilize the doppler shift or not, and does it
use delay-time demodulation of f-m signals for range determination?
Further questions are—will it work on multiple targets, and will it work
down to zero range?

It is hoped that the latter part of this chapter will have answered the
question asked at the beginning as to whether there are any uses for the
systems here described. Naturally, a general answer cannot be given
as to when c-w systems are indicated—we can only suggest a careful study
of the requirements and a comparison of the potentialities of the various
types of systems. Perhaps the only useful general remark is the obvious
one that c-w systems are most useful on problems where pulse systems
fail! For example, if one wants to measure a range of 10 ft a pulse
system would hardly be suggested; that described in Sec. 5-8 would
have no trouble. Also this c-w system will measure such short ranges
much more accurately than pulse systems. Or suppose the velocity of
a bullet is wanted—the system described in Sec. 5-6 measures such
quantities easily and directly. Or again, one may want simplicity—this
is provided by such a system which, when carried to the ultimate in this
direction, becomes the proximity fuze.

158

C-W RADAR SYSTEMS

[Sec. 512

Table 5.1.—Summary of

t = pulse width r maK = maximum range 8r — range discrimination

System

type

Repetition or
modulation
frequency

Simple doppler with audio
split into n bands (Sec.
5-6)

Range-measuring doppler < _ c_

system, two transmitted r 2r m ax

frequencies (Sec. 5-7)

F-m range measuring sys- c

tern (Sec. 5-8) r " 2 r mXi

Multiple target f-m system c

(Sec. 5-9) ” /r <<C 2/w

F-m system (Sec. 5T0) dop- _ c
pier band split into n 1 2 r

A-m doppler system (Sec.
511)

< 2r

Transmitter

spectrum

i 1

l »

— 1

h\.

~~ 1 ^

| 1

-1

h — -f.

111

4 6r

— 1

111

' U fr

-»£

~~i 1

r~ ?

— L

Number j
of side- ^
bands ___
1

frT r

for* fn

Sec. 5-12]

SUMMARY

159

System Characteristics

f r = modulation frequency or PRF fn = doppler frequency

Re¬

sponse

time

Informa¬

tion

rate

Number
of targets
possible

Ground

clutter

rejected?

Zero
range
possible ?

Frequency-

restrictions

Remarks

Jr*

Yes

' No

In 1946, maximum
clutter reduction
about 30 db.

Yes

If band is not split
w = l. Ground clut¬
ter filters are very
simple.

Yes

/*<£/,

In practice, noise limit
usually set by other
factors than noise
band.

Yes

fr> « J r fr

Clutter rejection not
known, probably not
extremely high.

r n
Trfo

f_R

Yes

}n <fr

Clutter rejection not
known, but probably
not extremely high.

Yes

Rejects extreme clut¬
ter; / n is bandwidth
of noise rejection
filter.

CHAPTER 6

THE GATHERING AND PRESENTATION OF RADAR DATA

By L. N. Ridenour, L. J. Haworth, B. V. Bowden, E. C. Pollard

61. Influence of Operational Requirements. 1 —The purpose of any
radar system is to present information on the positions of targets within
the volume of space it surveys. The nature of such targets, their
number, and the character of the information required about them will
depend profoundly on the function which the radar is called upon to
perform. For example, the radar altimeter used in aircraft deals with
only one target—the surface of the earth beneath the plane—and offers
only one datum—the minimum distance of the altimeter from that target.
A radar system used for control of air traffic near a landing field, on
the other hand, must display the range, bearing, and altitude of all
aircraft within or near the boundaries of the control zone. At a given
moment, there may be more than a hundred individual targets, for
each of which the radar must provide sufficiently accurate positional
information to enable controllers to issue prompt instructions to pilots.

Radar equipments suitable for such different purposes will present
wide differences in design. This chapter and the next deal with the
principal fundamental differences that appear in various conventional
pulse radar designs. In this chapter the effect of operational require¬
ments on the design of the radar itself is considered; in the next is dis¬
cussed the more difficult question of organizing the facilities and services
required to interpret and make use of the data provided by radar.

The most important and fundamental of the radar design differences
that arise from different functional requirements are those which con¬
cern the beam pattern produced by the antenna, the arrangements for
scanning a certain volume of space with that beam, and the indicator or
indicators necessary to display the positions of targets detected. Because
of the extremely close interrelationship among these three factors, and
because all three are principally determined by the functional aim of the
radar equipment, it would appear desirable to begin with a discussion of
the various radar functions, showing for each the choice of these three
factors which experience has so far recommended. Without an appro¬
priate introduction, however, such a treatment might be hopelessly
confusing. Accordingly, there follows a catalogue of existing indicator
1 By L. \. Ridenour.

160

Sec. 6-2]

DEFINITIONS

161

types, without attention to the functional requirement which has called
each into being, and without a description of the technical means of
realizing such indications. The latter subject is undertaken in Chap. 13.
The postponed discussion of radar functions, and of the choice of impor¬
tant radar properties to fit these functions, is found after this catalogue
of indicator types.

TYPES OF RADAR INDICATORS
By L. J. Haworth

6 2. Definitions.—The device that presents radar data in observable
form is called the indicator. It is usually a cathode-ray tube; alter¬
natively it may be a loudspeaker or telephone headset, a flashing light,
a moving-coil meter, or a pen-and-ink recorder.

The cathode-ray tube (CRT) permits an interpretation of electrical
phenomena in terms of a picture painted on a phosphorescent screen by a
sharply focused beam of electrons controlled in position and intensity by
electrical signals. It is capable of using and displaying many millions
of separate data per second. The geometrical expression which the CRT
gives to electrical phenomena is peculiarly appropriate to radar, because
a geometrical situation involving the various radar targets is precisely
what must usually be represented. Of the other devices mentioned as
possible indicators, only the pen-and-ink recorder is capable of giving
such a geometrical interpretation, and it is slow and cumbersome by
comparison.

Thus, in spite of certain inadequacies, a cathode-ray tube is used
as the radar indicator in all situations that involve any appreciable
target complexity. The picture presented on the tube face is called the
indication, the display, or the presentation. The tube itself is referred
to as the indicator, indicator tube, display tube, CRT, or scope. When a
tube presenting a particular form of display is to be identified, a descrip¬
tive adjective or code designation is prefixed to “scope.” The word
indicator is often extended to include devices and circuits auxiliary to
the cathode-ray tube.

Both magnetic and electrostatic cathode-ray tubes are used (Sec.
13T). In their design every effort has been made to achieve the
optimum in resolution, light intensity, deflection sensitivity, and com¬
pactness. The materials ( phosphors ) used in the screen are of particular
importance. If, as is usually the case, the scanning interrupts the picture
for longer than the retentivity time of the eye, it is necessary to introduce
persistence into the screen. Screens of various rates of decay are avail¬
able for this purpose. The detailed characteristics of the tubes, including
the screens, will be discussed in Secs. 13T to 13-3.

102 THE GATHERING AND PRESENTATION OF RADAR DATA [Sec. 6-2

In forming the displays, radar echo signals may be used either to
displace ( deflection-modulate ) the electron beam, as in the ordinary
oscilloscope, or to intensify ( intensity-modulate ) it, as is done in television.
Deflection modulation affords precise information about the strength
and character of the signals delivered by the receiver, but leaves only
one dimension of the tube face free to represent a geometrical quantity.
On the other hand, intensity modulation permits the presentation of a
two-dimensional figure on which the signals appear as bright spots or
patches, but offers only qualitative information about signal intensity.
The CRT screen cannot present any true three-dimensional picture,
of course; this is the most fundamental limitation of the cathode-ray
tube as a radar indicator. Under very simple conditions, it is possible
to present a third dimension in an understandable though unnatural
way, but in any complicated three-dimensional situation one is forced
to use more than one display.

The fundamental geometrical quantities involved in radar displays
are the spherical coordinates of the target measured from the origin
at the radar antenna: range, azimuth angle (or bearing), and elevation
angle. Practically every radar display uses one or two of these quanti¬
ties directly as coordinates on the tube face, or is a simple modification
of a display which does.

The vast majority of displays use as one coordinate the value of
slant range, its horizontal projection (ground range), or its vertical
projection (altitude). Since slant range is involved in every radar situa¬
tion, it inevitably appears in at least one display on every set. It is the
coordinate most frequently duplicated when more than one type of
display is used by a given radar set, partly because displays presenting
range have the greatest signal-to-noise discrimination, and partly for
geometrical reasons.

Range is displayed by causing the electron beam of the CRT to
move (sweep) across the tube at a uniform rate 1 starting fiom a given
point or line at a definite time in each pulse cycle. Thus, distances on
the tube face along this range sweep or time base are proportional to
increments of slant range. The scale factor relates distances on the
tube to actual range, and the sweep length is the distance represented;
both are determined by speed of the sweep. The origin of range may
be on or off the tube face; sometimes the start of the sweep is delayed for
some time after the instant of transmission of the outgoing pulse.

The angle in which the scanner is pointing, either in azimuth or
elevation, may enter into a display (1) directly as a polar angle, (2)

1 The range sweep must be nonuniform when it is desired to project range in a
plane not containing the radar set; as, for example, in the case of true ground mapping
on the indicator of an airborne radar.

Sec. 6-3]

SUMMARY OF INDICATOR TYPES

163

directly as a cartesian coordinate, or (3) as the basis for resolving a range
sweep in a particular direction. This will be further discussed in con¬
nection with specific types of display.

Indices or Scale Markers .—Both mechanical and electrical means
are used for making geometrical measurements on the displays.

In measuring range, “electronic” range markers are practically
always used. These consist of artificial video signals introduced into
the display by a precision timing circuit; thus, inaccuracies in the display
do not enter as sources of error in the measurements. Almost every
display entails a set of discrete, regularly spaced markers derived from
an oscillator properly phased with respect to the firing of the modulator.
Fairly accurate ranges can be read from these markers at a glance. In
many cases, however, interpolation errors are larger than can be tolerated;
the fixed markers are then supplemented by a manually controlled, con¬
tinuously movable, calibrated index. This index has the advantage of
extremely high precision, especially on an expanded sweep, but it requires
appreciable time in its use. Mechanical indices which move in front
of the CRT face are seldom used in measuring range.

For the determination of angle, it has been most usual in the past
to use mechanical indices: either a set of fixed indices engraved on a
transparent overlay, or a movable mechanical cursor. These can give
errors due to parallax and to inaccuracies in the display. More recently,
electronic indices have begun to replace mechanical range markers. A
discrete set of fixed indices, or a continuously variable index, may be
provided; for some techniques of display synthesis, the latter is not easy
to achieve.

The controls of movable markers, both of range and of angle, are
often connected to devices providing remote data transmission.

6-3. Summary of Indicator Types. —Many considerations enter into
the choice of the display geometry. In a three-dimensional problem, the
designer must decide how to divide the coordinates between two displays,
or how to present all the information on a single display, if this is feasible.
Even a two-dimensional display is complicated, and often involves con¬
flicting requirements, such as the need for high resolution in angle and
range without sacrifice in the total field of view. In some cases, the
needs can best be met by deliberately deforming the picture; in others
it may be necessary to use more than one display, either alternately on a
single tube or simultaneously on different ones.

Many different display schemes have been invented to deal with
these problems. The following summary, which classifies them according
to the spatial geometry represented, includes the important geometries
actually used. Although many others are possible, they have had little
or no practical application to date.

164 THE GATHERING AND PRESENTATION OF RADAR DATA [Sec. 0-4

I. One-dimensional deflection-modulated displays. These invari¬
ably present range. Two such displays on a single tube are
sometimes used to obtain directional information by comparing
signal intensities from two different beam lobes.

II. Two-dimensional intensity-modulated displays.

A. The representation of a horizontal or vertical plane.

1. Undeformed displays. Because of the nature of the
radar data these are usually in the form of polar plots of
range and angle (PPI).

2. Deformed displays.

a. Radial deformation of a polar plot created by a shift
in the range origin.

b. Linear deformation produced by “stretching” a polar
plot along one rectangular axis.

c. Rectangular plots of range and angle.

B. Rectangular plots of azimuth and elevation.

1. True displays which follow the antenna orientation.

2. Error indicators. (Such displays are not always intensity-
modulated.)

III. Three-dimensional intensity-modulated displays. These are
all modifications of uwo-dimensional displays which make use
of one or both of the coordinates on the tube face to present,
in a formalized way, information about the third dimension
being displayed.

6-4. One-dimensional Deflection-modulated Displays. —Since one¬
dimensional displays yield little geometrical information, their only
justification is that they permit the use of deflection modulation, which
gives a maximum of information about the intensity and form of the
echo signals. For this purpose, it is best to display the signals as a
function of time or range, and thus the only displays using deflection
modulation are those in which the deflections are applied perpendicular
to a range sweep (Fig. 6-1). This sweep may represent either a small
part or nearly all of the period between successive pulses. In the
former case, the particular range interval that appears on the display
is determined by the delay elapsing between the transmission of the
outgoing pulse and the starting of the range sweep.

The general classification “type A” is used to describe one-dimen¬
sional displays. An A-scope is universally used for observing radar
signals and various circuit waveforms in a radar set during test and
alignment. It may be either part of the permanent installation or a
piece of portable test equipment. The laboratory analogue of the
A-scope has come to be known as a “ synchroscope it is an indispensable
tool in the design and testing of electronic circuits.

Sec. 6 - 4 ) ONE-DIMENSIONAL DEFLECTION-MODULATED DISPLAYS 165

When the antenna of a modern narrow-beam radar is scanning, the
beam passes over each target in a comparatively short interval of time.
The resulting rapid appearance and disappearance of signals on an
A-scope makes this type of display confusing and of little use as a primary
indicator except for sets with very broad beams, extremely slow scanning
rates, or the operational function of “searchlighting”—following a
chosen target constantly. Even then, the chief utility of the A-scopc

Fia. 6-1.—A-scope. Range increases from left to right.

is as an instrument for accurate range determination, or for reading
certain types of coding of beacon signals (see Chap. 8).

Range Scopes .—The term “R-scope” (for range) is used to designate
several forms of modified A-scope that are used for accurate range¬
finding. In all of them, a greatly expanded sweep is combined with a
precision timing device. In some cases, the sweep delay is calibrated
only crudely, the entire precision being embodied in a timing circuit
which puts accurate range markers on the display itself. In others, the
delay circuit itself is a precision device, and forms a part of the complete

166 THE GATHERING AND PRESENTATION OF RADAR DATA [Sec. 6-4

timing equipment. The displays are sometimes subclassified in terms of
the particular type of electronic marker used (see Fig. 6-2).

Sometimes an R-sweep and an A-sweep are shown simultaneously
on the same tube by switching between them on alternate pulses. The
A-sweep is used for general surveillance of targets and for determining

the proper delay for the R-sweep, either by inspecting the range scale
or by displaying on the A-sweep an electronic marker which indicates
the setting of the R-sweep delay. Such an indicator is called an “ A-and-
R-scope.”

One form of deflection-modulated indicator which deserves special
mention is the J-scope, in which the sweep is circular and the deflections
Transmitted

(Sec. 6-14).

are applied radially by means of a central electrode (Fig. 6-3). The
circular sweep is derived by applying a properly phased precision sine
voltage in quadrature to two pairs of deflecting plates at right angles to
one another. The frequency of the sweep sinusoid may be many times
the pulse repetition frequency, in which case the intensity grid of the

Sec. 6-51 REPRESENTATION OF THE HORIZONTAL PLANE

167

CRT is used to blank the trace on all but one sweep cycle; a delayed
expanded sweep is thus produced (see Fig. 6-36).

“Pip-matching” Displays .—It is frequently useful to compare the
strength of the radar echoes received from a single target by means of
antennas whose patterns differ in direction (see, for example, Sec. 6T3).
For convenience of comparison, the two echoes are usually presented on
the same scope; they can be identified with the corresponding antenna
by either of two arrangements—the K-scope or the L-scope. The
K-scope (Fig. 6-4a) is so arranged that the range sweeps corresponding
to the two antennas start from different origins, with the result that the
echoes to be compared are side-by-side. In the L-scope, the signals
from the two antennas produce deflections of opposite sign, the range

(a) Side-by-side presentation (K-scope). (b) Back-to-back presentation (L-scope).
Signal return from the right lobe is the Signal return from the right lobe is the

stronger. stronger.

Fig. 6-4. —Pip-matching displays.

origin being common. The signals to be compared thus occur back-
to-back (Fig. 6-46).

6-6. Representation of the Horizontal Plane.—The large radius of
curvature of the earth and the shallowness of the layer of air above it in
which conventional aircraft are accustomed to fly make it useful to
project all signals from radar targets in a horizontal plane. Most radar
sets use a simple azimuth scan (with a beam that is fanned somewhat
in the vertical direction if aircraft are to be observed), and present their
data on a two-dimensional intensity-modulated display. Even when
target height is important, some' sort of range-azimuth display is usually
basic to the indication system. The third coordinate usually appears
in a separate presentation on another tube, often as a projection of
all targets on a vertical plane. Intensity-modulated displays of plane
surfaces constitute the most important class of radar indicators.

The Plan-position Indicator .—If the slant range and azimuth coordi¬
nates of the various targets in the field of view are represented, respec¬
tively, by distance from the center of a CRT and by azimuth on the
tube face, ths result is a map. Its only defect is the error introduced by
using slant range instead of ground range (that is, slant range times cosine

168 THE GATHERING AND PRESENTATION OF RADAR DATA [Sec. 6-5

of elevation angle). Except when viewing aircraft at very substantial
elevation angles, or when mapping the ground from a high-flying aircraft,
this error is imperceptible and can be neglected under practically all
circumstances.

The indicator used for the display just described is called the plan-
position indicator or PPI. 1 In the PPI, an outward range sweep is
rotated about the range origin in synchronism with the azimuthal
scanning of the antenna. Targets then appear in the proper directions
as well as at the proper relative distances from this origin and the result
is a map.

The origin of the PPI may be at the center of the cathode-ray tube,
giving an equal field of view in all directions. Frequently, however,

Fig. 6-5.—Off-center PPI.

it is displaced, sometimes far off the tube face, in order to give a maxi¬
mum expansion to a given region; such a display is called an off-center PPI
(Fig. 6-5). The expression sector display is often used when the dis¬
placement is extreme.

The PPI is the most widely used and versatile of all displays. In
presenting the information with which it deals, its only fundamental
shortcoming is that, in common with all maps or charts, it cannot simul¬
taneously possess a highly expanded scale and a large field of view.

The vertical analogue of the PPI may be formed by substituting ele¬
vation for azimuth angle. However, since only a restricted range of
elevation angle usually has interest, it is more customary to use distorted
displays for this purpose.

1 See Secs. 1315 to 13-18. The abbreviation “PPI” is used interchangeably to
represent both the display and the equipment (plan-position indicator). Abbrevia¬
tions for other types of indicators are used in the same way.

Sec. 6 - 5 ) REPRESENTATION OF THE HORIZONTAL PLANE

169

In spite of the usefulness of a true map display such as the PPI,
occasions arise in which it is not ideal. These situations usually involve
the need for providing high resolution or dispersion in some particular
coordinate without restricting the field of view too severely in other
dimensions. A number of types of deformed displays have been devised
for such purposes, and are particularly useful in dealing with point
targets.

Radial Deformation .—A polar plot such as the PPI can be deformed
radially by shifting the range origin, by using a nonlinear range scale, or
both. The first means has been widely used.

On a normal PPI it is difficult to determine accurately the direction
to a target whose range is a small fraction of that covered by the display.
This difficulty is often partly overcome by expanding the zero-range
origin of the PPI into a circle so that
the radius vector to the echo from a
nearby target is greatly increased.

Such an arrangement is known as an
open-center PPI. Range and bearing
retain their identities and their linear
scales. For the degree of center-open¬
ing ordinarily used, the deformation
introduced into the sizes, shapes, and
relative positions of the targets is
serious for only a fractional part of
the range portrayed. An open-center
PPI has been widely employed for
station-keeping and for homing on
such objects as ships, airplanes, run¬
ways, and the like. The open center
is switched in only a fraction of the time; for example, during the closing
stages of a homing operation.

It is sometimes desirable to provide an expanded range scale over an
interval at a distance from the radar site without sacrificing an all-round
view as an off-center PPI would do. This may be accomplished by
delaying and expanding the range sweep in an otherwise normal PPI so
that a ring-shaped area is collapsed into a solid circle. Because of the
technique used in producing it, this display is called a delayed PPI. As
in the open-center PPI, range and bearing retain their identities and their
linearity. The deformation is very great except at the extreme edge of
the display. The delayed PPI is used to increase the resolution on closely
spaced targets and on coded beacon signals, to facilitate accurate range
measurements, and to increase the signal-to-noise or signal-to-clutter
discernibility under some circumstances.

Elevation Angle

Fig. 6-6.—Stretched PPI. Two-mile
grid is shown by dashed lines.

170 THE GATHERING AND PRESENTATION OF RADAR DATA [Sec. 6-5

Linear Deformation. —A deformed display of considerable utility,
especially in the vertical plane, can be formed by “stretching” a polar
plot in one rectangular dimension as though it were on a sheet of rubber.
On such a display, the cartesian coordinates parallel and perpendicular
to the axis of stretch retain their original meaning and their linearity, but
they have different scale factors. Straight lines remain straight but,
except for those parallel to the coordinate axes, their directions are
changed. Circles of equal range appear as ellipses with their major axes
in the direction of the stretch.

In the horizontal plane this geometry, called the stretched PPI 1 (Fig.

6-6), is useful principally in con¬
nection with the control from a
remote point of aircraft approach¬
ing a landing, or ships navigating
a channel. The stretching, done
in a direction perpendicular to the
desired course, aids greatly in de¬
tecting slight deviations therefrom.

This technique finds its great¬
est utility in the vertical plane
where vertical stretching is used
to enhance the accuracy of aircraft
height determination (see discus¬
sion of RHI, Sec. 6-6).

Rectangular Presentation of
Range and Angle. —A plane sur¬
face is often represented in a de¬
formed manner by combining
range and angle in cartesian rather
than in polar coordinates. This
is accomplished by moving a range sweep laterally across the tube face in
synchronism with the antenna motion so that the origin is stretched out
into a line.

In range and azimuth these rectangular displays are of two different
sorts:

1. Displays in which no attempt is made to minimize the deformation,
either because it is unimportant in the particular circumstances,
or because certain advantages can be gained by neglecting it. Any
desired range interval and azimuthal sector may be covered,
although in practice more than 180° is rarely used. The display
is always normalized to make optimum use of the tube face.

Fig. 6*7.—B-scope. The azimuth inter¬
val displayed is 180°; the range marks are
2 miles apart.

1 This has sometimes been called, erroneously, an “expanded azimuth” display.

Sec. 6-6]

PLANE DISPLAYS INVOLVING ELEVATION

171

Range is always plotted vertically, and at short range the resolu¬
tion in angle is far greater than that afforded by the PPI. This
display, called “type B,” (shown in Figs. 6 7 and 6-8) is used in
situations where the chief considerations are the range and bearing
of point targets or groups of targets, with little or no importance
attached to the shapes of extended targets or the relative locations
of widely separated targets. It is especially useful in homing, and
in telling plots of range and bearing for recording elsewhere in polar
form.

2. Displays in which the desired angular field of view is so small that
the distortion can be made negligible by proper normalization of

(a) 150-mile sweep, normal PPI with grid (6) 100-mile sweep, B-scan, zero delay,
squares.

Fig. 6-8.—Distortion caused by B-scope display.

the range and angle scales. Such a display, known as a micro-D,
is simply a substitute for a PPI sector; it is used either because it is
technically easier to attain, or because the same indicator is alter¬
nately used for a regular type B display. Proper normalization
requires that the angular dispersion be kept proportional to the
range to the center of the display.

The vertical analogue of the type B display, known as “type E,” will
be described in the next section.

6-6. Plane Displays Involving Elevation. —One rarely desires to know
the elevation angle or altitude of an aircraft target without also requiring
its range and bearing. Simultaneous azimuth and elevation information
can be obtained by two-dimensional scanning with a single antenna, by
the V-beam principle (Sec. 6T2), or by the use of separate radar systems
scanning respectively in azimuth and in elevation. In the last case, the

172 THE GATHERING AND PRESENTATION OF RADAR DATA [Sec. 6-6

elevation scanner must be adjustable in azimuth, since otherwise its beam
must be so wide that range performance is poor or target identification
is difficult.

Two-dimensional scanning limits range performance. The average
power reaching a point target is reduced below that corresponding to a
simple azimuth scan by a factor approximately equal to the number of

Fig. 6-9. —Range-height indicator (RHI).

beamwidths scanned vertically. The signal-to-noise discernibility on a
PPI or a B-scope is reduced by this same factor, if the total scanning
times are equal in the two cases.

The Range-height Indicator (RHI ).—The RHI, shown in Fig. 6-9, is
the elevation-angle analogue of the stretched PPI, as indicated in the
last section. Target range is displayed as a horizontal coordinate and

Sec. 6-6j

PLANE DISPLAYS INVOLVING ELEVATION

173

the display is expanded in the vertical dimension, so that the height
interval to be covered occupies approximately the same distance on the
tube face. Lines of constant height are horizontal and equally spaced.
Arrangements are sometimes made to move the range origin off the tube
face to allow expansion of a region of interest.

If the height-finding antenna is required to scan over an appreciable
range of azimuth angles, the RHI is usu¬
ally blanked except during a relatively
narrow azimuth sector, in order to improve
the ratio of signal to noise and to avoid
confusion between targets at different
azimuths. This sector can be chosen by
adjustment of a calibrated control.

The RHI is always used in conjunc¬
tion with a PPI or other display of the
horizontal plane; usually this auxiliary
indicator obtains its data from another
radar set. The signals from a given tar¬
get are correlated in the two displays on
the basis of range and azimuth position. In some cases the height-finding
antenna searchlights in azimuth and is manually aimed in the proper
direction. If it scans in azimuth, the center of the sector which is shown
on the RHI is indicated by a mechanical cursor on the PPI of the search
set.

The E-scope .—-The E-scope is a rectangular display in which range

is the x-coordinate and elevation
angle the y-coordinate. Lines of
constant height are hyperbolas
(Fig. 6T0). As in the case of the
B-scope, a delayed range sweep is
often used to allow range expan¬
sion. The elevation analogue of
the micro-B (Sec. 6 5) has found no
application, since the distortion of
the E-scope is not particularly
harmful and, by allowing it to occur,
the dispersion in the elevation coor¬
dinate can be normalized to make the most effective use of the tube face.
In some older sets, the E-scope is used for height indication, but its dis¬
tortion and its poor height dispersion at large ranges make it inferior to
the RHI for this purpose.

The C-scope .—The type C display presents the azimuth and elevation
angle coordinates of the scanner as rectangular coordinates on the tube

^Groui

echo*

Fig. 611.—C-scope.

Fig. 6'10. —E-scope. Lines of
equal height are shown dotted.

174 THE GATHERING AND PRESENTATION OF RADAR DATA [Sec. 6-7

face (Fig. 6-11). It can be used in conjunction with a PPI or a type B
display as an aid to homing (Sec. 6-13). This display has the great dis¬
advantage that its signal-to-noise discrimination is very poor if signals
are displayed for an appreciable fraction of the pulse cycle (see Chap. 2).
For this reason, the C-scope is usually blanked except for a short range
interval including the signal of interest. Initial recognition of the target
signal is accomplished on the other display, and the proper range setting
for the C-scope display interval is determined either by inspection or by
displaying on the search tube an electronic marker derived from the
C-scope brightening signal.

The V-beam height indicator is an example of the type of display con¬
sidered in this section, but its description is deferred to Sec. 612.

6-7. Three-dimensional Displays. —In spite of the fact that the face
of the cathode-ray is two-dimensional, two conventionalized three-

antenna beam

(a) Double-dot indicator. (6) Pattern of spiral scan (c) Radial time base (RTB)

used with displays indicator,

shown at (a) and (c).

Fig. 6-12.—Three-dimensional displays. A, B, and C are targets.

dimensional displays [as distinguished from error indicators (Sec. 6-8)]
have been successfully used in situations involving relatively few targets.

The “ Double-dot ” Display. —A modified type B presentation on which
elevation angle is roughly indicated is known as the ‘‘double-dot ” display.
On alternate range sweeps the origin of the pattern is moved to the right
and left respectively by a fixed amount (Fig. 612a). On the sweeps
corresponding to the right-hand position the origin is simultaneously
shifted vertically by an amount proportional to the sine of the elevation
angle. Any single echo therefore appears in two neighboring positions,
and the slope of the line joining the two “dots” is a rough measure of
elevation angle which is accurate to two or three degrees under the usual
circumstances of use. This display has been used in air-to-air homing
(AN/A PS-6).

The “Radial Time Base’’ Indicator. —The radial-time-base indicator
is a three-dimensional display which, like the double-dot display, is best

Sec. 6-9]

EARLY AIRCRAFT-WARNING RADAR

175

suited for use with a spiral scan. A range sweep moves from the center
of the tube in a direction corresponding to the projection of the antenna
beam on a plane perpendicular to the axis of scanning (Fig. 6-12c). The
echoes therefore appear at radial distances corresponding to their range.
If the target is on the symmetry axis of the scan, it is equally illuminated
at all “spin” angles and the echo appears as a full circle. If it is far off
axis it is illuminated only through a narrow spin angle (target B) and
the arc on the display is short. Target C indicates an intermediate
case. The display is surprisingly easy to interpret after a short period of
observation.

6-8. Error Indicators. —-A cathode-ray tube may be used as a radar
indicator in a quite different, way from those so far described; that is, as a
meter on which to display various forms of intelligence. One common
use of an error indicator is to indicate accuracy of pointing in connection
with a conical scan. The signal intensity is combined electrically with
the scanning information to provide voltages proportional to (or at least
increasing with) the pointing error in
both azimuth and elevation. These
voltages are used to deflect the spot.

A departure of the spot from the tube
center indicates the direction and, to
a qualitative degree at least, the mag¬
nitude of the pointing error. The
radar signal is sometimes used to in¬
tensify the spot in order to distinguish
between perfect pointing and no tar¬
get. Range can be indicated by caus¬
ing the spot to grow “wings” whose
length is some rough inverse measure of the range. In this form (Fig.
G-13) the indication gives to a surprising degree the illusion of an actual
aircraft which apparently grows larger as it approaches.

EXAMPLES OF THE MAJOR OPERATIONAL REQUIREMENTS

6-9. Early Aircraft-warning Radar. 1 —The British Home Chain .—The

first radar to have actual combat use was the British CH (Chain, Home)
equipment. Work was begun in 1936 toward setting up five stations,
about 25 miles apart, to protect London and the Thames estuary, and by
the time war broke out in 1939 this Chain had been extended to cover the
greater part of the south and east coasts of England and Scotland.
During the next few years the Chain was extended and its equipment and
performance were improved. In spite of the introduction of more modern
and efficient equipment, the Chain provided the basis of the British

1 By B. V. Bowden and L. N. Ridenour.

Elevation

error

Fig. 6-13.—Spot error indicator with
wings to indicate target range.

176 THE GATHERING AND PRESENTATION OF RADAR DATA [Sec. 6 9

reporting system for the greater part of the war. At the very end of the
war the system was used to plot V-2 rockets. The great success of the
equipment, which saved the country from defeat during the Battle of
Britain, had an important effect on the course of radar development. It
called attention to the revolutionary usefulness of radar in modern air
warfare, but at the same time it tended to freeze operational thinking
concerning radar along lines of the static defense which was all that the
CH stations could provide-

The main Chain operated at frequencies between 22 and 28 Mc/sec.
In spite of the disadvantages inevitable in any system operating on so
low a frequency, the choice was made deliberately after consideration of
the tubes and techniques available at the time.

“Throughout the whole of the development period the small team who were
responsible ruthlessly sacrificed all refinements, elegancies and versatilities in
the desperate need for something to be going on with. They never turned aside
from their cult of the third best—“The best never comes, the second best comes
too late.’’ 1

At the frequency used, strong reflections from the ionosphere occur,
and an extremely low repetition rate of 25 pps was used in order to ensure
that ionospheric echoes were not confused with echoes from aircraft
targets. The repetition rate could be reduced to 12.5 pps when iono¬
spheric disturbances were unusually troublesome.

The pulse width could be varied from 6 to about 25 jusec and the
receiver bandwidth could be changed from 50 to 500 kc/sec. In normal
operation the pulse length was about 12 /isec and the bandwidth 150
kc/sec. The final design made use of continuously evacuated transmit¬
ting tubes with uncoated tungsten filaments, whose c-w power output was
about 80 kw. Peak pulse power using these tubes was about 150 kw;
later, it was increased to about one megawatt. Both transmitters and
receivers were massive and elaborate. They were housed in separate
bombproof buildings, usually about half a mile apart.

Separate antennas were used for transmitting and receiving. The
main transmitting antenna was an array, usually of six dipoles with
suitable tuned reflectors, hung between two gantries on a 350-ft steel
tower. These towers were usually installed in sets of three in order to
provide spare antennas and standby frequencies. Radiation from the
transmitting antenna floodlit a quarter-sphere in front of the station, the
greater part of the energy being confined within 20° of the horizontal
and within approximately +50° of the main “line of shoot.” Enough

'Sir R. A. Watson-Watt, “Radar in War and in Peace,” Nature, 156, 319-324,
(1945).

Sec. 6-9]

EARLY AIRCRAFT-WARNING RADAR

177

energy was radiated backwards to make it uncertain, without special
arrangements, whether a target was in front of or behind a station.

The main receiving antenna consisted of a pair (or a stack of pairs)
of crossed dipoles, mounted on 240-ft wooden towers. Balanced pairs
of concentric feeders connected the dipoles to the field coils of a goniom¬
eter whose rotor was connected to the receiver. The final display was
on a 12-in. A-scope. The range of a target was determined from a scale
on the oscilloscope, and its azimuth by rotating the goniometer until the
echo disappeared. Ambiguities of 180° were resolved by the use of

Fig. 6-14—Typical elevation pattern of CH radar, east coast of England, 1939. Wave¬
length = 10.1 meters.

reflectors mounted near the receiving antennas. These reflectors could
be switched in or out of circuit by remote control from the ground. From
their effect on the echo, the operator could deduce whether the target
was in front of or behind the station.

The performance of CH stations was controlled by the reflections
from the ground of both the transmitted and the received signals. The
antenna patterns of the transmitting and receiving arrays were not
identical and there were large gaps in the vertical coverage of the stations.
In order to minimize the importance of the gaps, separate auxiliary
“gap-filling” transmitting and receiving arrays were installed to allow
aircraft to be followed through the gaps produced by the main arrays
(see Figs. 6T4 and 6T5). It was desirable that the ground surrounding a
station should be flat for several miles in every direction; few stations had
really ’deal sites. Even when all possible precautions had been taken,

178 THE GATHERING AND PRESENTATION OF RADAR DATA [Sec. 6 9

station performance was never predictable from theory. It was always
necessary to “calibrate” a station by an elaborate series of test flights.

The maximum reliable range of a CH station was usually about 120
to 150 miles on single aircraft, but the range depended very much on the
skill of the operator and of the maintenance crew as well as on meteoro-

40,000
I 30,000

£ 20,000
op

x 10,000

Range in miles

Fig. 6*15.—Polar diagram of typical CH station for reliable pickup of single fighter
aircraft along the line of sight. Solid line represents main arrays; broken line represents
gap-filling arrays.

logical conditions. As early as 1941 a Photographic Reconnaissance
Spitfire, flying at about 40,000 ft, was plotted by the CH station at
Canewdon, just, north of the Thames estuary, as it flew almost all the way
to Genoa at a maximum range of over 450 miles.

Height-finding was performed by making use of the lobe pattern of

the receiving antennas. Figure 6T6
shows the vertical pattern produced
by two receiving antennas, respec¬
tively at 220 and 90 ft above ground.
If one compares the signals received
in these two antennas as a function of
angle of elevation, one obtains a curve
shown dotted in Fig. 6-16. It follows
that, by measuring the signal ratio,
it is sometimes possible to deduce
the angle of elevation of the target.
The comparison was performed by
means of the goniometer already
described.

Under normal circumstances, the
field coils of the goniometer were
connected to two dipoles about 220 ft above the ground. By means of a
switch, one goniometer coil was connected to a dipole at 220 ft, the other
to a dipole at about 90 ft. By turning the goniometer to give minimum
signal, the angle of elevation of the target could be determined and hence
its height could be deduced (see Fig. 6T7).

Elevation angle in degrees

Fig. 616. —Relative signal strengths
from CH height-finding antennas.
Wavelength = 13.22 meters, (a) Two
dipoles, mean height 220 ft. ( b ) One
dipole at 90 ft. (c) Ratio of (a) to (f>)
on an arbitrary scale.

10 20 30 40 50 60 70 80 90 100 110 120

Sec. 6-91

EARLY AIRCRAFT-WARNING RADAR

179

Measurements of angles of elevation above about 7° were ambiguous
on this so-called “A ” system, and measurements of angles below about 1°
were inaccurate owing to the “flatness” of the height curve for these
small angles. The maximum usable angle of elevation was extended by
using two receiving antennas 90 ft and 45 ft high respectively (the “ B”
system). Figure 6T7 shows the goniometer readings for the A and B
systems as a function of angle of elevation. The curves are plotted for a
flat site and-for antennas perfectly matched to their feeders. In practice,
the height curves for all stations were verified by an elaborate series of
test flights. Owing to irregularities of sites the height curves varied
considerably with azimuth, with the result that it was sometimes neces¬

sary to use half a dozen different height calibrations. Some stations
could measure height only in one or two favorable azimuths.

The operations involved in applying azimuth errors and interpreting
height measurements were performed automatically by a system of
standard telephone selector switches and relays. The operator measured
range by a pointer on the tube, azimuth by turning the goniometer to
give zero response from the echo. She 1 then pressed a button and the
grid reference (Chap. 7) of the target appeared on a board. The operator
then switched to height-finding, turned the goniometer again and pressed
a button, whereupon the height was displayed in front of the teller. If
the height measurement was ambiguous or unreliable, that fact was shown
by the machine, and the operator could try again on the “B” height
system. Operational use of radar information is discussed in Chap. 7.

The shortcomings of the CH system are fairly clear. Its long
wavelength necessitated the use of large and expensive towers. There

1 After 1940 almost all operators were women.

180 THE GATHERING AND PRESENTATION OF RADAR DATA [Sec. 6 9

were large gaps in its vertical coverage (Figs. 6-14 and 6'15). The range
on low-flying aircraft was poor. The system was supplemented in 1940
by 200-Me/sec equipment, the so-called “CHL” (Chain, Home, Low)
system. It was often very difficult to find sites that were flat enough
for stations. Since the station at Dover was on a 400-ft cliff and Ventnor
was on a cliff 1000 ft above the sea, it was impossible for these stations to
measure height at all. The processes involved in deducing the plan posi¬
tion and the height of an aircraft were complicated and not very reliable.
The maximum traffic-handling capacity was low (a good operator could
pass about 6 plots per minute), and the system could not keep track of
large numbers of independently routed aircraft. Nevertheless, forma¬
tions of aircraft were plotted reliably, and the number of aircraft in ti
formation could be estimated by an experienced operator. With all its
imperfections, this system was the basis of the British radar defense for
the greater part of the war.

The CXAM .—While the British Home Chain was being designed and
installed, the Army and Navy development agencies in the United States
were independently developing pulse radar equipment. The earliest
service equipment to be commercially manufactured was the CXAM
radar, designed at the Naval Research Laboratory. A laboratory-built
prototype of this set Vvas tested at sea during battle maneuvers in early
1939, aboard the U.S.S. New York, and its performance was so promising
that a contract was let in October 1939 for the manufacture of six sets of
similar equipment.

The CXAM was operationally quite different from the CH. Instead
of using separate, fixed, broad-beam transmitting and receiving arrays,
it employed a common antenna for transmitting and receiving. To pro¬
duce as narrow as beam as possible, it operated at the then ultrahigh
frequency of 195 Mc/sec, and employed a “mattress” array of dipoles
with reflectors, giving a gain of 40 and a beam 14° wide in azimuth by
about 70° in elevation. The antenna could be rotated in azimuth at a
speed of 5 rpm, or manually trained to follow a particular target. The
peak pulse power was 15 kw, the pulsewidth 3 nsec, and the repetition
rate 1640 pps. Range against bombers was about 70 miles, against
fighters about 50 miles.

The display was an A-scope in which the trace was lengthened by
causing the sweep to take place from left to right across the tube, then
drop down and return from right to leu. Range was estimated with the
help of marks on the face of the tube; bearing was determined as
the direction of antenna-pointing which yielded maximum signal. The
height of targets could be estimated with the help of nulls in the vertical
antenna pattern (Sec. 6T1).

Despite its early design and its lack of adequate coverage against low-

Sec. 6-9]

EARLY AIRCRAFT-WARNING RADAR

181

flying aircraft, this simple, rugged equipment proved highly satisfactory
in service use. It was the direct forerunner of the later shipborne long-
range air-search radar equipments (SA, SC and its various redesigns, SK
and its redesigns) used on large ships until the end of the war.

SCR -270 and SCR-271 .—The early efforts of the U.S. Army Signal
Corps to design service radar equipment were in the direction of produc-

Fig. 6-18.—SCR-270D.

ing an equipment for antiaircraft fire control and searchlight control
(SCR-268; see Sec. 6T4). In May 1937 the Air Corps requested the
development of a “long-range detector and tracker.” One laboratory
version of the resulting equipment was demonstrated in November 1939
and showed a range of more than 100 miles on bombers. In August 1940
a contract for quantity production of this equipment was let.

182 THE GATHERING AND PRESENTATION OF RADAR DATA [Sec. 610

The set was built both for mobile use (SCR-270) and for fixed-station
installation (SCR-271). During the general advance in radar technique,
the set went through many detailed changes and improvements and was
still in active use at the close of the Japanese war.

The SCR-270 1 and the CXAM are quite similar in their operating fea¬
tures. The SCR-270 operates at a frequency of 106 Mc/sec, has a peak
power of 100 kw, a pulsewidth from 10 to 25 psec, and a reliable range
against single bombing aircraft of more than 100 miles. The repetition
rate is 621 pps. The same antenna is used for both transmission and
reception. This antenna (Fig. 6T8) consists of a dipole array originally
four dipoles wide and nine high, with a reflector; the antenna gain is 140
and the beamwidths 28° in azimuth and 10° in elevation. Provision is
made either for continuous rotation of the antenna at 1 rpm or for manual
training to maximize target signals.

The SCR-270 has an A-scope display, with a control for so varying
the start of the sweep that a selected target signal can be brought under a
marker on the face of the tube; a scale on the phasing control then indi¬
cates target range directly. Target bearing is determined by reading off
the antenna azimuth when the echo signal from the target in question
appears to be strongest. The azimuth accuracy depends on proper
siting, as in the case of all radar making use of ground reflections, and
attainable accuracy in practice is about + 4°. Height-finding can be
performed by the method of nulls (Sec. 6T1).

Later models of this set include, among other improvements, an antenna
giving a beam narrower in azimuth, and a PPI indicator. The simplicity,
reliability, and ruggedness of the SCR-270 made it a very useful and very
widely used equipment despite its great bulk and weight, its poor low-
angle coverage, its vulnerability to ground clutter in anything less than a
very carefully chosen site, its lack of range resolution and azimuth dis¬
crimination, and its low traffic-handling capacity.

6-10. PPI Radar for Search, Control, and Pilotage. 2 —In the last
section, an important historical development has been traced. The
first radar sets used fixed antennas and floodlighting technique, and
required that a manipulation be performed to find the azimuth of each
target. Next were designed relatively narrow-beam, continuously scan¬
ning radars, in which each target in the field of view is displayed period¬
ically, so that its azimuth and range can be read off at regular intervals.
A further step was made with the development of the plan-position indi¬
cator, or PPI, which, although the radar beam was still narrow and still

1 Since the radar design of the SCR-270 does not differ from that of the SCR-271,
the designation SCR-270 will be used, as a matter of convenience, to stand for either
equipment.

2 By L, N. Ridenour.

Sec. 610 ] PPI RADAR FOR SEARCH, CONTROL, AND PILOTAGE 183

showed instantaneously only those targets located in a narrow azimuth
sector, made use of the persistent property of CRT screen phosphors to
preserve from one scan to another the target signals returned on the
most recent scan. The PPI thus presents a continuous map-like display
of all targets in the field of view of its radar, and permits attention to be
concentrated on particular targets without the penalty of losing sight of
the general situation.

It is interesting to notice that, before the advent of the PPI, users of
such equipment as the CXAM and the SCR-270 frequently constructed
a plan display with pencil and paper, plotting in polar coordinates the
targets whose range and azimuth were called off by the radar operator.
Further, skilled operators of such sets developed an ability to form, by
watching the A-scope, a sort of mental PPI picture of the radar targets,
remembering from scan to scan their ranges and bearing angles. When
the PPI became available, the operator was released from this necessity,
and could apply his skills to a more sophisticated mental appreciation
of the target situation; for example, a good PPI operator will often keep
in his mind the directions in which important targets are moving.

With the exception of special-purpose sets all radar equipment designed
in 1941 or later contained one or more PPI scopes. In many types of
equipment the use of the PPI is fundamental to the purpose of the radar.
PPI radar sets can be divided into three classes: land-based, shipborne,
or airborne.

Ground-based PPI sets are usually employed for the detection and
plotting of aircraft, either to give early warning of enemy air activity, or
to control friendly aircraft by radio instructions, or both. Mounted on
shore, such sets can also be used for plotting ship traffic to permit warning
and control, but this use is simply a two-dimensional case of the same
problem as that involved in plotting aircraft.

In wartime, radar sets on shipboard must provide air-search and con¬
trol facilities, and in addition must give a display of surface targets, to
permit station-keeping in formation and pilotage in narrow waters under
conditions of poor visibility. In peacetime, usually only the surface-
search function is of importance. Because of the different beam-shape
requirements, separate radar systems are ordinarily used for air search
and for surface search.

Airborne radar equipments employing a PPI are used for pilotage in
the vicinity of shorelines or over land. This pilotage may be of a general
navigational character, as it always is in peacetime and usually is in war;
or it may be as precise as the limitations of the radar will permit, for the
purpose of blind bombing of a radar target.

The narrow beam provided by a microwave radar is important in all
these cases. In ground radar, a narrow beam permits the detailed resolu-

184 THE GATHERING AND PRESENTATION OF RADAR DATA [Sec. 611

tion of a complicated air situation, and also is beneficial in reducing the
effects of ground clutter. Ship radar for displaying surface targets will
show greater range, other things being equal, the shorter the wavelength
used. This is a result of interference between the direct beam and the
beam reflected from the water surface (Sec. 2T2). The greater azimuth
resolution provided by a sharper beam is also useful in resolving com¬
plicated target situations. The only drawback of microwave radar for
ship search is the resultant narrowing of the beam in elevation; in order to
keep the rolling of the ship from tilting the beam away from the surface
of the sea, either the antenna mount must be mechanically stabilized
(Chap. 9), or the vertical dimensions of the antenna must be reduced to
fan the beam sufficiently in elevation to take account of roll. In air¬
borne PPI radar, the attainment of sufficiently good display detail to
permit navigation over land, away from distinctive shorelines, demands
the use of microwave frequencies. In fact, a considerable premium is
placed on attainment of the narrowest azimuth beamwidth possible.
Antenna stabilization is also desirable in aircraft, to correct for the effects
of changes in attitude; but it is so costly in weight and complication that
it has been seldom used.

Typical examples of PPI radar systems intended for ground and for
airborne use are analyzed in detail in Chap. 15.

6-11. Height-finding Involving Ground Reflection. 1 —The height of
an aircraft target is usually determined by finding separately its range
and its angle of elevation, and then solving the equation H — R sin e.
In the wartime use of radar, height was such an important datum
that considerable ingenuity was expended on the problem of its
measurement.

The resulting methods can be roughly separated into two classes
depending on whether the reflection of energy from the level surface
surrounding the radar antenna is important to the scheme of height-find¬
ing used. In this section are considered methods which do involve
ground (or sea) reflection; in the next, free-space beam methods which
do not.

If the antenna of a radar of medium wavelength, for example, about
one meter, is less than about fifty wavelengths above the ground, the
reflected energy from the part of the beam that strikes the ground will
produce maxima and minima in the elevation pattern. These are shown
for a representative case in Fig. 6T9.

Null Readings .—In a pattern such as that shown in Fig. 619, the
range at which an aircraft first appears on the screen depends upon the
height of the aircraft. If the antenna pattern is known, height may be
estimated from range of first appearance. If the course of the aircraft

1 By E. C. Pollard and L. N. Ridenour.

Sec. 611] HEIGHT-FINDING INVOLVING GROUND REFLECTION 185

is approximately directly toward the station, the range at which the first
fade is seen is also determined by the target height. If several fade
points are determined, the height can be inferred with better accuracy.
This method has been used extensively with the 200-Mc/sec aircraft-
search radar used on naval vessels. It is especially useful with this type
of radar because the elevation pattern can be well known (the ocean is a
good reflector, and the antenna height is determined by the class of ship
and not by the shape of the terrain), and because a radial approach to a
task force is generally chosen by either enemy or friend.

Height-finding by nulls, however, has inherent drawbacks which
seriously reduce its accuracy in operational use. The elevation pattern
of a ground-based set must be carefully calibrated experimentally,
because the reflection coefficient of the surrounding ground will determine
the pattern, and because uneven ground gives different elevation patterns
at different azimuths. Further, changes in the aspect presented to the
radar by the aircraft may cause
great changes in the echo strength.

Finally, variations in the atmos¬
pheric refractive index can cause
large variations in the amount of
radiation falling on the ground or
water surface surrounding the
radar and thus appreciably change
the pattern. 1 Despite these diffi¬
culties, if there is plenty of friendly
air traffic and if radio contact can be used to enable a continual check on
height accuracy, adept radar plotters can give heights accurate to within
one thousand feet more than half the time by the observation of signal
fades. The method is slow; a reading cannot be made in less time than
that required for a plane to fly through several nulls of the pattern. This
drawback, and the elaborate calibration necessary at an overland site,
have led to the development of other height-finding means, even for long¬
wave radar sets.

Signal Comparison .—A more rapid and convenient means of height¬
finding which is also based on the existence of maxima and minima in t he
elevation pattern of a long-wave radar employing ground reflection is
signal comparison. Two Or more antenna systems with different eleva¬
tion patterns are provided at a single radar station, and the intensity of
the echo received on one antenna is compared with that received on
another. The comparison may be made either by measuring the vector

1 Since refraction of one-half degree is possible, and since variations of echo strength
due to aspect can be 12 db, altitude errors of several thousand feet can occur even in
the favorable case of sea reflection.

Fig. 6-19. —Typical elevation lobe pattern.

186 THE GATHERING AND PRESENTATION OF RADAR DATA [Sec. 6 11

First lobe, antenna 1

Fig. 6-20.—Elevation coverage diagram.

resultant of simultaneously received signals (as is done in the CH by
means of a goniometer; see Sec. 6-9), or by presenting alternately received
signals side-by-side in a type K display and estimating visually their ratio
in height.

The British Type 7 equipment is the most widely used radar exploiting

this signal-comparison principle.
A copy of this equipment built in
Canada for the United States is
called the SCR-588; American-built
redesigns of the same basic equip¬
ment are the SCR-527 and the
SCR-627. The antenna of this set.
is placed very close to the ground
in such a way that the beam is
tilted up in elevation and low-angle
coverage deliberately sacrificed. A
lobe pattern such as that shown
in Fig. 6-20 is thus produced.

The lobes are few in number and
very wide. A second antenna,
placed at a different height, produces a second series of lobes which overlap
those of the first antenna. The echo strength for one lobe system is com¬
pared with that for the lobe system from the other antenna. A type K
display system is used which shows the two responses side-by-side on a
12-in. scope. From the relative in¬
tensities and the range of the aircraft,
height can be deduced.

For either lobe pattern, the electric
field strength at the target depends
on the phase difference between the
direct and reflected beams, and so
will vary nearly sinusoidally with the
altitude of the target. Figure 6-21
is drawn for antenna heights of 35
ft and 23 ft, on the assumption of
sinusoidal variation. It shows the
ratio between the signal strength in the lower beam and that in the upper
as a function of elevation angle.

The ratio varies slowly for small elevation angles, then rapidly as the
lower lobe just touches the aircraft—in this case at an elevation angle of
about 4°. By estimating the signal-strength ratio correct to 10 per cent,
the angle of elevation can be told with an average accuracy of about one-
third degree, corresponding to a height error at 50 miles of ± 1000 ft.

Fig. 6-21.—Ratio of signals in lower and
upper beams.

Sec. 612 ] HEIGHT-FINDING WITH A FREE-SPACE BEAM

187

The angular range through which this height-finding scheme is useful
is shown in Fig. 6-21 by dotted lines. At low angles the variation of ratio
with angle is far too slow. At angles near 4° the variation is fast, but
the illumination of the plane by the lower beam may be so weak that no
echo is obtained, and therefore no height can be inferred. If both the
antennas are nearer the ground, the effective angle is increased, but the
beams are both tipped up so much that coverage on aircraft at low and
medium altitude is sacrificed. Even in the case we have considered, an
aircraft 10,000 ft high and 50 miles away, or one 5000 ft high at a range
of 25 miles, would fall in the unmeasurable class.

To overcome these limitations, a variety of overlapping elevation
lobe patterns are made available by providing a variety of antennas with
phase and antiphase feeding. This additional complexity increases the
time required to find height, since if the operator cannot guess which
combination of antennas is suitable, a wrong choice makes it necessary
for him to wait for a full 360° rotation of the antenna mount before he
can try a better pair.

In addition to the elaboration necessary in equipment for height¬
finding by this method, siting is also a problem. A suitable site should
be level within a few feet for a half-mile radius around the radar. Even
sea reflection can be troublesome, because tides cause a profound change
in the calibration of the station as a height finder. For these reasons, a
free-space-beam height finder, not depending on ground reflection, is
usually preferred.

6-12. Height-finding with a Free-space Beam. 1 Searchlighting .—The
simplest form of free-space-beam height finder is one which measures
elevation angle of the desired target directly, by pointing an antenna
producing a narrow beam directly at the target and measuring the eleva¬
tion angle at the antenna mount. This technique is called “search¬
lighting.” Even with cent imeter wavelengths, beam widths attainable
with antenna reflectors of practicable size (a few degrees) are large in
comparison with the accuracy desired in the measurement of elevation
angle (about a tenth of a degree) for height-finding purposes. Therefore,
target height is not usually determined by directing the beam at the
target simply by maximizing the echo.

Instead, arrangements are made for shifting the beam rapidly in ele¬
vation angle by an amount which may be, typically, a third of a beam-
width, and comparing the echo signal received in one position with that
in the other. When the two signals are equal, the bisector of the angle
between the two positions of the beam is pointed directly at the target.
The signals from a given target may be compared for the two positions
of the beam by presenting them side-by-side on a type K indicator or

1 By E. C. Pollard, L. N. Ridenour, and D. C. Soper.

188 THE GATHERING AND PRESENTATION OF RADAR DATA [Sec. 6-12

back-to-back on a type L indicator, or by using integrating methods of
signal comparison and error display.

A simple means for moving the beam in elevation angle is to rotate
the beam rapidly about an axis which makes a small angle with the center
line of the beam; this is called “conical scanning.” It will be seen that a
conical scan permits the simultaneous determination not only of the
elevation error in pointing the axis of the scan at the target, but also of
the azimuth error in such pointing. Full consideration of this method
for angular tracking of a single target is deferred to Sec. 6-14, but it will
be useful here to describe a few principal features of a radar that employs
conical scan solely for the purpose of height-finding.

This principle was used in the British CMH, a mobile 10-cm equip¬
ment designed specifically for height-finding. It used a 6-ft dish, a
power of 500 kw, and was capable of measuring heights to within + 500 ft.

The aircraft to be measured was followed manually in range with the
aid of an electronic marker on the range trace. Two other operators fol¬
lowed manual!}' in azimuth and elevation. The range and elevation
settings were used to operate an automatic height indicator which could
be placed in a remote position adjacent to a PPI fed by an auxiliary search
radar.

Only a few of these equipments were built owing to progress in the
development of a centimetric scanning system, and to the inherent inabil¬
ity of the CMH to find height on more than one target at a time. The
SCR-615 was a similar U.S. equipment, except that it was designed as a
fixed installation and employed an 8-ft dish.

The SM equipment used by the U.S. Navy was perhaps the most
widely used of allied radar sets in this category. It was employed in
conjunction with suitable PPI radar for ship control of aircraft. Its
wavelength is 10.7 cm, and it employs an antenna reflector 8 ft in diam¬
eter. The waveguide feed used is a little off the axis of the paraboloid,
so that the beam, whose width is 3°, is off axis by 1°. The feed is rotated
to produce the conical scan. Pulses from the upper half of the antenna
rotation are compared with those from the lower half by means of inte¬
grating circuits, and the output difference is used to displace the spot of an
error indicator (Sec. 6-8). A PPI is provided for general reporting, and
two range scopes, one covering the full range of the set and one an
expanded A-scope, make it possible to determine target range and to
eliminate from the signal-comparison circuits all echoes except those from
the target whose altitude is being determined.

In operation, either a helical scan (Sec. 9’7) or a continuous rotation in
azimuth with manually controlled elevation can be used in searching for
targets. The helical scan can be set to cover any 12° in elevation angle
in the range from 3° below to 75° above the horizon. When it is desired

Sec. 6-12] HEIGHT-FINDING WITH A FREE-SPACE BEAM

189

to find height on a target, the antenna is stopped and manually kept
pointed in the target azimuth. The target is located on the full-range
A-scope, and the range interval covered by the expanded A-scope adjusted
to include the target. A portion of the sweep of the expanded A-scope
is deflected downward to form a “ditch” (Fig. 6-2c). Only signals
received during the range interval represented by this "ditch” are fed
to the integrating circuits which control the spot error indicator. The
setting of the expanded A-scope is adjusted until the desired signal is in
the “ditch,” and the antenna pointing is adjusted to center the error
indicator. When this has been done, the elevation angle of the line of
sight to the target can be read off repeater dials which indicate the eleva¬
tion angle of the mount. The altitude of the target, which is computed
electrically as the product of range and sine of elevation angle, is shown
directly on a meter calibrated in feet.

When SM equipment is used on shipboard, angles between the
antenna and the structure of the ship must be properly corrected with
respect to a stable vertical, maintained by a gyro, in order to yield the
true angles which would have been measured with respect to a level
structure. Considerable attention has been paid to the stabilization of
radar antennas on ships and aircraft, and to the data correction that can
sometimes be used as a substitute (see Chap. 9).

Elevation Scanning .—The height-finding methods so far described
are all limited in accuracy, in speed of height-reading, or in the number of
targets which can be dealt with at once by a single height-finding radar.
The advantages of a system in which a narrow beam scans in elevation
and the signals are displayed directly on an intensity-modulated tube
whose coordinates are derived from range and elevation angle are appar¬
ent. These very important advantages were clear before the microwave
radar art had advanced to the point where it was possible to obtain nar¬
row beams and adequate range performance with reasonably small
antenna structures.

As a result, the British developed a system operated at 200 Mc/sec
which provided elevation scanning with a fixed antenna. It was called
Variable Elevation Beam (VEB). Two versions were developed, one
using a 240-ft mast and the other a 120-ft mast, the latter being intended
for rapid installation. Such tall structures were necessary in order to
obtain a narrow beamwidth in elevation at this low frequency.

The antenna system on a 240-ft mast consists of nine groups, each
of eight horizontal dipoles, spaced vertically one above another. This
version scans over a range of elevation angle from f° to 7j°. The beam-
tilting is achieved by altering the relative phasing of the groups of
dipoles; each group is fed from a mechanical phase shifter mounted in
the center of the mast. The banks of dipoles can be tilted mechanically

190 THE GATHERING AND PRESENTATION OF RADAR DATA [Sec. 612

to move the scanning range to the elevation interval from 7?° to 15°.
Elevation can be read to an accuracy of ±0.15° and readings can be
obtained to a maximum range of about 70 miles.

The 120-ft svstem consists of nine groups of four dipoles each, stacked
vertically. Its scan covers the range of elevation angles from lf° to 15°.
Elevation angle readings can be obtained to an accuracy of +0.3° out to
about 55 miles range.

The horizontal antenna pattern of both sets is a fixed wide beam
covering approximately 60° on either side of a predetermined “line of
shoot.”

The indicator is an E-scope in which a horizontal intensity-modulated
range sweep moves vertically up the tube in synchronism with the move-

Fig. 6-22.—British A.M.E.S. Type 13 height finder

ment of the radar beam. Signals appear as vertical lines at a certain
range along the trace centered about the elevation angle of the target.
Calculation of height from range and elevation angle is performed
automatically by the selector switch and relay equipment, used in CH
stations (Sec. 6-9). The range and elevation of the target are set into
the computer by the operator, who adjusts range and angle markers to
cross at the center of the target signal on the scope, “'he computer
indicates target height in numerals on a lamp display.

Development of the microwave art permitted the design of elevation-
scanning height finders which, unlike the VEB, could be made mobile.
The first such set to be used operationally was the British Type 13. The
reason for the late appearance of this very successful height finder is the
technical difficulty of illuminating an antenna reflector of large aperture
ratio. This is accomplished in the Type 13 by illuminating a double
“cheese” (Fig. 6-22) by means of a horn feed (Chap. 9). Although side

Sec. 612 ] HEIGHT-FINDING WITH A FREE-SPACE BEAM

191

lobes are not objectionable in this antenna, it displays considerable fre¬
quency sensitivity. A standing-wave voltage ratio of 1.33 (Chap. 11) is
encountered for a frequency change of 2 per cent. The beamwidths are
1° in the vertical dimension and 6° in the horizontal dimension. The
pulse width is 2 /xsec, the output power 500 kw.

In operation, the antenna is moved up and down in the expected
azimuth of search at a rate of one oscillation in ten seconds. An RHI
display is used (Fig. 6-23). Because of the slow rate of scan, it is impera¬
tive to use a second radar to determine the approximate direction of the
target. The Type 7 equipment was widely used for this function. The
azimuth position of the Type 13 radar is shown on the PPI of the Type 7
by means of a beam of light pro¬
jected from behind the phospho¬
rescent screen of the PPI. This
light is yellowish and does not affect
the persistence of the radar signals
on the PPI. In addition there is a
color contrast between it and the
echoes. By rotating the antenna
of the Type 13 until this “azicator”
line cuts the center of the signal on
the PPI, the Type 13 can be cor¬
rectly enough pointed to display the
desired target. The beamwidth of
6° is chosen to be wide enough to permit Type 13 operation with a PPI
radar having very poor resolution.

A similar American set (AN/TPS-10) is lighter and simpler since it
operates at 3 cm. This enables the antenna size to be reduced to 10 by
3 ft with the very high gain of 18,000. The range is over 50 miles on a
four-motored aircraft, although the radar set uses only 60-kw output
power at 1-Msec pulse width and 1000 pps. The antenna can be oscillated
once per second. The beamwidths are 0.7° in elevation and 2° in azi¬
muth. This last is much smaller than was at first thought feasible; it
was argued that so small an azimuth beamwidth would render search for
the target laborious. It has proved, however, to be no operational
limitation.

Height-finding by such a set is reasonably accurate. The results of a
calibration flight with an experimental model of the AN/TPS-10 are
shown in Fig. 6-24. Relative height is accurate to about ±300 ft under
favorable conditions. Absolute height is more difficult to find accurately
by radar, because of the bending of the beam by atmospheric refraction,
which varies from time to time. Fortunately, relative height is usually
sufficient for aircraft control. Further, it is generally possible to keep

20 15

10 “

f 10 20 30 40 50 60 70

/ Range in miles

Ground
echoes

Fig. 6-23.- -llange-height indicator of
Type 13.

192 THE GATHERING AND PRESENTATION OF RADAR DATA [Sec. 612

track of refraction conditions by talking to pilots of aircraft seen on the
radar, and checking radar height readings with their altimeters.

Combined Plan and Height Systems .—Despite the speed, convenience,
and accuracy of the elevation-scanning height finders just described, these
sets are merely auxiliary to a search radar. Equipments that provide
plan and height information continuously on all targets in the field of
view, using a single antenna system, are obviously preferable. The
limitations discussed in Chap. 4 on the range out to which a substantial
area can be rapidly scanned preclude the design of a single radar system
which will give both plan and height information with the necessary
accuracy, as often as is desirable, and out to a range limited only by the

optical horizon.

Two or more radar systems can
be combined to allow' continuous
and rapid indication of both plan
position and height of all targets in
the field of view'. One example of
such a radar is a ship-based set
w'hich combines a conventional PPI
radar with an elevation-scan height
finder of advanced design.
Another, working on quite a differ¬
ent principle, is the V-beam radar,
which reduces the measurement of
height to two measurements of tar¬
get azimuth.

The ship radar uses a search set and a height finder w'hose antennas
occupy the same pedestal. The search set has a beamwidth in azimuth
of 1.5° and elevation coverage up to 15°. The height finder antenna is
15 ft high by 5 ft wide, fed at 8.9-cm wavelength by a special feed (Sec.
9T6) which can cause the beam to scan at ten oscillations per second.
The beamwidth in elevation is 1° and in azimuth 4°. The height finder
antenna feed is so arranged that the pulses are distributed uniformly
throughout the angle of scan, and not concentrated at the upper and
low'er angles as they are by the mechanical oscillation used in the sets just
described. As a result, the antenna can be rotated at 4 rpm and height¬
finding to a range of 50 statute miles is quite possible. A 12° range of
elevation angle can be covered.

The antenna is shown in Fig. 9-31. The display console is shown in
Fig. 6-25. A three-fold indication scheme is used. One indicator gives
the general PPI picture and a second gives an expansion in range and
azimuth angle w'hich enables detailed control to be accomplished. The
third indicator is a range-height indicator. The RHI is brightened for a

Ground range in miles

Fig. 6-24.—Calibration of height readings
of AN/TPS-10.

Sec. 612] HEIGHT-FINDING WITH A FREE-SPACE BEAM 193

selected range of azimuth angle which corresponds to that shown on the
expanded range-azimuth indicator, so that the aircraft under detailed
observation can be recognized on the RHI. Four or more display con¬
soles, each with a full complement of indicators, can be operated inde¬
pendently and at the same time from a single radar.

The fundamental principle of the V-beam radar is to reduce the obser¬
vation of elevation angle to a double observation of azimuth angle. The

Fig. 6-25.—Console of ship-based height finding radar.

second observation of azimuth is made by a beam slanted at 45° to the
ordinary search beam of a ground PPI radar. The two beams form a
V-6haped trough.

Figure 6-26 (see also Fig. 41) shows the two beams and the direction
of rotation of the antenna mount. The 45° V reproduces the value of
the height as the horizontal distance between the vertical and slant beams
at the appropriate range and height. This is expressible in terms of D,
the ground range to the target. If A<p is the angle turned by the mount,

194 THE GATHERING AND PRESENTATION OF RADAR DATA [Sec. 612

h = D sin A <j>. But D- = R* — A 2 , so that

_ R sin A <f>

(1 + sin 2 A

This simple relation permits height to be found if the target range
and the difference angle can be determined. There is a danger that at

Fig. 6-26.—Schematic view of V-beam principle. For clarity, vertical and slant beams are
shown without the 10° separation in azimuth which is used in practice.

low elevations the two signals from the vertical and slant beams might
be displayed so close together that no height can be found. This problem
is eliminated by introducing a fixed separation of 10° between the beams,
so that there is a 10° separation between the signals even from a target
at zero altitude. The indicator is designed around the general principle
of a B-seope in that range is presented against angle. The simplest form
of indicator has range along the horizontal axis and A <f> on the vertical

axis (Fig. 6-27). Suppose a target
appears at A on the vertical beam
at an azimuth selected by the
operator. Video output from the
vertical beam appears on the scope
for 10° of azimuth rotation cen¬
tered on the selected azimuth. It
is then blanked out and slant video
substituted. If the target is at
zero elevation, the slant beam will
illuminate it 10° later, at A'. If
the target has a definite height,
the slant beam will rotate further
before illuminating it and the
signal will actually appear at B, as
shown. A movable overlay superimposed on the scope face is set so that
its baseline bisects the first signal at A The 10° delay position is marked
by a second line, which serves as the zero-height line for a succession of
constant-height lines which appear as drawn. Height is estimated
directly from the face of the scope. The two signals from a single target
(e.g., A and B) always appear at the same range.

, Slant-beam
video signals

Vertical-beam
video signals

Range in miles

Fig. 6-27.—Simple V-beam indicator,
of constant height are shown.

Lines

196 THE GATHERING AND PRESENTATION OF RADAR DATA [Sec. 613

This type of height finder is free from the range limitation which
arises from the scanning loss of a rapidly scanning system. The V-beam
can, in principle, find height to any range where a search set of the same
antenna size can detect aircraft. Heights on single aircraft out to 140
miles have been recorded.

The set is shown in Fig. 6-28. The two antenna reflectors are 25 by
10 ft. The vertical sheet of radiation is obtained by three separate
transmitters feeding a horn and a series of dipoles. The slant beam uses
only two transmitters, since early-warning range is ordinarily not needed
on the slant beam which is intended for height-finding.

The results of height calibrations show that heights can be called
rapidly to an accuracy of +1000 ft and, with care, to ±500 ft. If an
average is taken, better results can be obtained.

6-13. Homing. 1 —The use of airborne radar to guide an aircraft to its
target was extremely important during the war. Long-wave radar
installed in aircraft is scarcely capable of performing any function more
complicated than homing, since the enormous size of an antenna giving a
beam sharp enough to produce a map-type display precludes its use in
aircraft. Fortunately for the wartime development of airborne radar,
homing is a tactically important function both in the attack of shipping
by aircraft and in the interception of hostile aircraft by defending
fighters. Sets for both purposes operating near 200 Mc/sec were exten¬
sively used during the war.

Homing on a Surface Target .—The simpler of the two problems is that
of the detection and interception of shipping by patrol aircraft. Since
targets are known to be on the surface of the sea, homing information
need be supplied only in azimuth. The first operationally successful
aircraft-to-surface-vessel, ASV, radar was the British ASV Mark II. A
counterpart of this equipment was manufactured in the United States,
being called SCR-521 by the Army and ASE by the Navy.

The SCR-521 operates at a frequency of 176 Mc/sec. Two sets of
antennas are provided giving different beam patterns (Fig. 6-29); one
pattern is used for search and the other for homing. Each pattern con¬
sists of a left and a right lobe. In the search position these lobes extend
broadside to the airplane; in the homing position they extend nearly
straight ahead, so that they overlap to a considerable extent. The exact
design of these antennas underwent a complicated series of changes. In
some equipments separate antennas were used for transmission and for
reception, and in others both functions were carried out with a common
antenna. In all cases, however, the general coverage and arrangement
of the beams were those shown in Fig. 6-29.

The radar receiver is rapidly switched from the left to the right mem-

1 B.v L. N. Ridenour.

Sec. 613]

HOMING

197

ber of the pair of antennas in use, and the radar echoes are displayed on
an L-scope in which signals coining from the left antenna cause a displace¬
ment of the trace toward the left, and signals from the right antenna
displace the trace to the right (Fig. 6-4). The range sweep is linear,
upward from the bottom of the scope, and the range is estimated by an
engraved scale in front of the tube.

On the search antennas, a given target shows either on the left antenna
or on the right, depending on its location with respect to the aircraft,
never on both. On the homing antennas, however, because of the over¬
lapping coverage of the two beams, a target will show a signal at the same
range both to the left and to the right of the center line. A comparison
of the strength of the two returns shows the radar observer in which
direction course must be altered to home on the target. Care must be
taken in antenna installation to make sure that the axis of equal signal
coincides with the direction of flight of the aircraft. “Squint,” which

Left antenna

Fig. 6 29.—Beam patterns

of ASV Mark II (SCR-521). (a) Search antenna pattern.

(b) Homing antenna pattern.

results from improper installation or trimming of antennas, has the same
operational effect as crabbing of the aircraft in a cross-wind; in either
case, the operator notices that the relative signal strength of the left and
right echoes changes when the aircraft is steady on a compass course
initially chosen to give equal signals. A skillful operator can allow for
this effect and choose a course on which the signals, though not equal, do
not change relative to one another when the course is held. This, regard¬
less of squint or crabbing, is a true interception course.

The first radar beacons (Chap. 8) were designed for use with this
equipment. The type L display is just as well suited to homing on a
beacon as it is to homing on a radar target, and the navigational aid
provided by beacons was very useful in bringing aircraft home after long
sea patrols.

A very similar equipment operationally, but of greatly reduced total
weight, has been widely used by the U.S. Navy. Referred to as the
ASB, it operates on 515 Mc/sec, at which frequency a dipole becomes
small enough to allow the Yagi arrays used as antennas to be mounted
on a rotating mechanism that permits them to be pointed broadside for
search, or turned forward for homing, at the will of the operator (Fig.

198 THE GATHERING AND PRESENTATION OF RADAR DATA [Sec. 6 13

6-30). A single Yagi on each side is used as a common transmitting and
receiving antenna. The indication and the method of use of this equip¬
ment are the same as those of the ASV Mark II.

With the introduction of microwave airborne radar, sea-search equip¬
ment giving a map-type indication became practicable. Pilotage within
50 to 100 miles of islands or coastlines is very greatly facilitated by such

Fig. 6-30.—ASB antenna.

radar equipment, and the advantage of coverage of the complete field of
view by such scanning radar (instead of coverage of the two sectors
viewed by the equipments just described) is important in sizing up a com¬
plicated target situation. Only the bulk and weight of early microwave
airborne radar militated against its use for sea search; these difficulties
have now been overcome.

Since homing, as well as search, is important, special provision is

Sec. 613]

HOMING

199

usually made to facilitate homing in a sea-search radar. This usually
takes the form of a provision for “sector” scan and a modified indicator.
Sector scan is, as its name implies, an arrangement for causing the antenna
to scan back and forth across a desired sector, sometimes one centered
dead ahead of the aircraft, and sometimes one that is adjustable at the
will of the operator. The indicator provisions for homing are of either
of two types: the set may have a type B display, which facilitates homing
because the condition for an interception course is that the target signal
approach down a vertical line of constant azimuth, or it may have an
open-center PPI. In the latter, the target follows along a radius as the
range is closed on an interception course; the open center reduces the
crowding of signals at short ranges and makes homing easier. A movable
engraved marker or electronic index showing constant azimuth is usually
provided with either type of display to aid in homing.

The principal wartime American microwave ASV sets were:

1. The SCR-717, a 10-cm equipment whose antenna is a 30-in. parab¬
oloid arranged either for continuous rotation or for sector scan,
at the will of the operator, and whose indicator is, in different
models, either a type B or a PPI arranged to permit center-opening.

2. The ASG, a very similar equipment made for the Navy by another
manufacturer, which offers only PPI display.

3. The AN/APS-15, a 3-cm radar with optional sector scan and with
PPI display, designed for overland bombing but used for sea search
when its “cosecant-squared” antenna (Sec. 2-5) providing high-
altitude coverage is replaced by one designed for about 5000 ft,
the optimum altitude for sea search.

4. A series of Navy equipments operating at 3 cm and designed for
the primary purpose of homing.

These latter sets are the ASD, an improved redesign of the ASD called
the ASD-1 or the AN/APS-3, and the ASH or AN/APS-4, a set similar
to the other two, but representing a very complete redesign with the
principal object of reducing bulk and weight. The 18-in. paraboloid
antennas of the ASD and the AN/APS-3 are mounted in a nacelle faired
into the leading edge of the wing of a single-engined aircraft. (Fig.
6-31.) All of the AN/APS-4 except the indicator and the controls is
mounted in a “bomb” hung under the plane on the conventional bomb
shackles (Fig. 6-32). The paraboloid antenna reflector of the AN/APS-4
is 14 in. in diameter. In all these equipments, the 360° azimuth scan of
the Army equipments is replaced by a wide sector scan centered along the
line-of-flight of the aircraft, and covering about 160° in all. At the will
of the operator, this scan can be replaced by a narrow sector scan exe¬
cuted more rapidly. Type B indication only is provided; provision is

Fig. 6-31.—Scanner housing of AN/APS-6 in wing of F6F. The installation of AN/APS-3
in single-engine carrier-based torpedo bombers is identical in external appearance.

Fig. 6-32.—Units of AN/APS-4. Covers, radome, and fairing of main unit are removed.
In use, main unit is suspended from bracket shown at bottom in this view.

Homing on Aircraft .—During the war, defensive nightfighters
equipped with radar were developed as a reply to night bombing attacks.
The homing problem faced by the Aircraft Interception, AI, radar used
for this purpose is more difficult than that presented in the sea-search

200 THE GATHERING AND PRESENTATION OF RADAR DATA [Sec. 6-13

made for expansion of the sector dead ahead when homing is being carried
out. In these sets, the general mapping functions of microwave radar
have been sacrificed in favor of the utmost simplicity and ease in carrying
out the homing function.

Sec. 613 ]

HOMING

201

application, since the target speed is much higher (and much more nearly
that of the intercepting aircraft), and since homing must be carried out in
two dimensions instead of one.

An early AI equipment was designed by the British as an extension
to AI of the design principles of ASV Mark II. It was designated AI
Mark IV by the British; a similar system made for the U.S. Army
by an American manufacturer was called SCR-540. In this set, which
operated near 200 M c/sec, a single transmitting antenna sent a broad
lobe in the forward direction from the aircraft. Two pairs of receiving
antennas were provided; one pair produced overlapping lobes like the
“homing” lobes of the ASV Mark II, to give an indication (also identical
with that of the ASV Mark II) of the homing error in azimuth. The
other pair of lobes was used to measure homing error in elevation angle;
they overlapped exactly when viewed from above the airplane, but one
was displaced slightly above the center line of the airplane and the other
slightly below the center line. Elevation homing error was shown on a
second indicator exactly like that of the ASV Mark II, turned through
90° so that the range sweep occurred horizontally from left to right.
Signals from the upper lobe displaced the trace upward; those from the
lower lobe displaced it downward. The receiver was rapidly switched
to each of the four receiving antennas in turn, and the display correspond¬
ingly switched to the proper deflection plate of the appropriate indicator
tube. Range could be read either on the azimuth tube or on the eleva¬
tion tube. The arrangement of the receiving antenna patterns and of
the indications is shown in Fig. 6-33.

The principal operational limitation of this equipment was a result
of the fact that very broad beams were produced by the single-dipole-and-
reflector antennas used. These broad beams gave strong reflections
from the ground beneath the aircraft, restricting the maximum range at
which aircraft echoes could be seen to less than the altitude at which the
Al-equipped fighter was flying. In the case of ASV operating on 200
Mc/sec, similar returns from the sea were experienced, but the returns
from ship targets were so strong that signals were sought and tracked at
ranges beyond the sea return. Aircraft echoes w r ere many times weaker,
so that aircraft could be seen only at ranges shorter than the ground
return.

It was clear that the best hope of escaping this limitation w'as to make
use of a sharper beam in AI equipment, and since the maximum antenna
size was limited by the necessity of aircraft installation, considerable
effort was exerted to develop a microwave AI. The American equipment
which resulted is the SCR-720. In this equipment, a 29-in. paraboloid
reflector rotates continuously in azimuth and is slowly tilted in elevation.
The helical scan thus produced covers an elevation interval of 25°. The

202 THE GATHERING AND PRESENTATION OF RADAR DATA [Sec. 613

9.1-cm wavelength used gives a beamwidth of 10°, which is sharp enough
to allow a target on the same level as that of the Al-equipped aircraft to
be followed out to several times the altitude common to the two aircraft
without undue difficulty from ground return.

Two types of indicator are provided. The radar operator has a
B-scope which shows targets on a range-azimuth display; this is provided
with a movable marker that enables the operator to feed to the other
indicator—a C-scope showing azimuth and elevation—only the video
signals in a range interval centered on the range at which the marker is

Left receiving
antenna

'ransmitted
beam
receiving
antenna

Upper receiving
antenna

■Transmitted
beam

Lower receiving
antenna

Beam patterns
(Top view)

Beam patterns
(Side view)

Altitude

Ground return

Target echo:
left antenna

Altitude

■Target echo;
right antenna

Range to
target

Target echo;
upper receiving
antenna

Ground return

Target echo;
lower receiving
antenna

Azimuth indicator Elevation indicator

Fig. 6-33.—Beam patterns and indication of British AI Mark IV (SCR-540).

set. The unfavorable signal-to-noise characteristics of the C-scope are
thus somewhat mitigated, and the C-scope, which is repeated for the
benefit of the pilot, displays only the desired target. A range meter
operated by the position of the radar operator's movable marker is also
provided to enable the pilot to gauge the progress of the interception.

The SCR-720 has been used with success both by the RAF and the
AAF.

An airborne automatic tracking radar—essentially a light version of
the SCR-584 described in the next section—was designed for AI use and
manufactured in small quantity. Though it was operationally very
satisfactory and was highly regarded by nightfighter pilots who flew with
it, it was never used in the war, principally because of the low priority
put by the AAF on night air defense after 1942. This set was designated
SCR-702, AN APG-1, and (made by another manufacturer) AN APG-2.

The difficult problem of providing AI equipment for single-engine,
single-seat, carrier-based Navy nightfighters was solved in a marginally

Sec. 614] PRECISION TRACKING OF A SINGLE TARGET 203

satisfactory way by the AIA equipment and its redesigned successor, the
AN/APS-6. This 3-cm equipment has an 18-in. reflector which is
housed in a wing nacelle in the same fashion as that of the AN/APS-3.
As this reflector is rotated at 1200 rpm about an axis passing through its
feed and parallel to the line of flight of the aircraft, the paraboloid is
slowly tilted from a position in which its axis coincides with the axis of
rotation to a position in which there is a 60° angle between these axes.
Because of the pattern thus traced out in space by the beam (Fig. 6-126),
this is called a spiral scan; a complete scan takes 4 sec. The display
used for sea-rch is the “double dot” indicator described in Sec. 6-7
(Fig. 612a).

In the last stages of a homing operation, the assumption is made that
the pilot can safely concentrate all his attention on his target. Turning
a switch then changes both the scan and the indication. The tilt of the
antenna with respect to the axis of its rotation is fixed at 3°, resulting in a
conical scan. Two voltages, respectively linear with the azimuth error
and with the elevation error in pointing the axis of the conical scan
toward the target, are applied to a spot error indicator of the type
described in Sec. 6-8. The pilot completes the interception by keeping
the spot centered on his scope, and closing the range until the wings of
the spot have grown to the desired size.

6-14. Precision Tracking of a Single Target. 1 —During the war, con¬
siderable effort was expended in the design of radar for highly precise
position-finding on one target at a time. This tracking w r as ordinarily
intended to permit the control of fire against such a target, but as the
w T ar drew to a close, it was also used for detailed control of the maneuvers
of the target by radio instructions from a controller at a ground station.
This w r as done to permit blind bombing by fight-bombers too small to
carry a radar set and its operator, or to enable an aircraft not equipped
with radar to make a blind landing approach on instructions from a con¬
troller at a ground radar. The latter use has, and w-ill probably continue
to have, a considerable peacetime importance.

Lobe-switching and Pip-matching .—The first radar set intended for
precision tracking of a single target w as the SCR-268, a laboratory proto¬
type of which was formally demonstrated to the Secretary of War in
May 1937. The problem of accurately tracking a moving target with an
antenna that can be elevated and trained is similar to the problem of
homing with the help of fixed antennas on a movable vehicle, and the
same techniques are useful. Lobe switching, which has been described
in the last Section, is employed by the SCR-268 for angle-error determi¬
nation; in fact, the SCR-268 was the earliest production radar to use
this technique. The general appearance of the set is shown in Fig. 6-34.

1 By E. C. Pollard and L. N. Ridenour.

Fig. 6-34.—SCR-268 in operation.

Sec. 614] PRECISION TRACKING OF A SINGLE TARGET

205

At the operating frequency of 205 Me/sec, a 4 by 4 array of dipoles with
reflectors gives a beam about 24° wide in azimuth and in elevation.
Return echoes are received on two separate antenna arrays, each with its
own receiver. One array, six dipoles wide by four high, gives information
to an azimuth scope; the other, two dipoles wide and six high, provides
signals to an elevation scope. The receiving arrays have two separate
feeds arranged to produce different phase relations between the elements
of the array. Thus, by switching the azimuth receiver from one feed to
another, the beam pattern of the receiving antenna can be switched from
one to the other of two overlapping lobes equally displaced in azimuth on
opposite sides of the normal to the antenna array. Similar switching
arrangements are provided for the elevation antenna and its receiving
channel.

The antennas are mounted on a single cross arm, which rotates in
azimuth with a central pedestal enclosing the radar circuits and can be
turned about its own axis to elevate the arrays. Three operators, each
with a scope, ride with the cross arm as it turns. A range operator is
provided with an A-scope having a movable marker w'hich he keeps on
the signal being tracked. His rotation of the range handwheel feeds
range information to a “height converter,” a computing mechanism
employing a three-dimensional cam to combine slant range and elevation
angle in such a w'ay that continuous target altitude information is pro¬
duced. Rotation of the range handwheel also brings the signal being
tracked into the center of the azimuth and elevation display tubes.
Each of these tubes is manned by an operator provided with a handwheel
which moves the antenna in the appropriate angular coordinate. The
display is type K (Fig. 6-4). It is the duty of the azimuth operator to
keep the two signal “pips” in the center of his scope matched in height
by turning his handwheel; the elevation operator has a similar task.

The maximum design range of the set is 40,000 yards, and the repeti¬
tion rate is 4098 pps. With a power output greater than 50 kw and a
pulse width of 7 to 15 ^sec, the set is very conservatively designed, and
can track targets much beyond its rated range. Angular accuracies
attainable in practice with this equipment, about ± 1°, are too poor to
permit good blind antiaircraft fire, and because of ground reflections the
equipment suffers from severe errors in reading elevation at angles smaller
than about 10°. However, this versatile, rugged, and readily mobile
equipment was available in quantity early in the war, and served many
useful roles, being used for fire control, short-range search and warning,
and searchlight control.

Conical Scan and Error Indication .—In a situation where not more than
one target at a time is expected in the radar field of view, the equipment
necessary to track a target can be considerably simplified. Such a case

Fig. 6*35.—Scanner of AN/APG-15 in tail turret of B-29.

these circumstances, the bomber can be protected by a simple, short-
range radar equipment mounted in the tail turret. The B-29 was
equipped with a radar of this sort, the AN/APG-15. Figure 6-35 shows
the antenna installation.

The equipment operated at 12 cm, and had a 12-in. dish giving a
beam width of about 25°. This beamwidth was sufficient to give warn-

■ -saw*™

206 THE GATHERING AND PRESENTATION OF RADAR DATA [Sec. 6-14

arose in the past war in connection with the defense of bombing aircraft
against nightfighters. The limitations of AI radar were such that a
coordinated attack on a single bomber by more than one nightfighter was
not possible, and the only practicable attack was the stem chase. Under

Sec. G 14] PRECISION TRACKING OF A SINGLE TARGET

207

ing coverage of the tail cone without the necessity for scanning. The
beam was conically scanned by rotating the reflector about an axis which
made an angle of 2.5° with its own. Commutators were mounted on the
shaft of the antenna rotation mechanism so that signals from the upper
half of the scan could be integrated and compared with those from the
lower half; similarly, signals from the left half of the scan were compared
with those from the right. The resulting error voltages were used to
deflect the spot of a CRT used as an error indicator. An automatic cir¬
cuit searched in range in the absence of a target, and locked on and
tracked a target when an echo was encountered within the 2000-vd
coverage of the set. This range circuit was used to brighten the spot
only when a target was in range, in order to distinguish between correct
pointing and the absence of a target. It also caused the target spot to
grow horizontal “wings” whose spread increased as the range grew
shorter, in order to provide an indication of range to the gunner (see
Fig. 6 13).

The axis of the conical scan was aligned with the guns so that only
point-blank fire with no lead was possible. This was done because the
lead required in countering the usual nightfighter approach is negligible.
The indicator was so arranged that its display was projected into the
reflector sight, enabling the gunner to use the same technique for either
optical or radar tracking. This equipment became available so late in
the war that it had substantially no operational use, but its proving-
ground tests indicated that its performance would have been quite satis¬
factory. The attainable angular accuracy was about ±0.5°.

The AN/APG-15 was unusual in that a triode, the “lighthouse”
tube, was used as a pulsed oscillator. At the low pulse power used (about
500 watts), this enabled transmitter, receiver, and the necessary rectifier-
filter power supplies to be housed in one compact unit, shown in Fig. 6 36.

Automatic Angle Tracking .—Shortcomings of the SCR-268 as a fire-
control position finder arose mainly from the use of a relatively long
wavelength which resulted in broad beams from antennas of any reason¬
able size. When microwave radar became practicable with the develop¬
ment of the cavity magnetron, one of the immediate applications of the
new technique was an antiaircraft position finder. The most widely used
and generally successful of the resulting equipments was the SCR-584.

Before beginning precision tracking of a single target, a radar that is
to serve as the only equipment of an antiaircraft battery must execute a
general search in order to locate targets that are to be tracked and
engaged. No auxiliary long-wave radar search equipment was provided
with the SCR-584. Instead, the 6-ft antenna reflector was helically
scanned, and targets presented on a PPI whose maximum range was
60,000 yd. A range of elevation angles up to 10° was covered by the

208 THE GATHERING AND PRESENTATION OF RADAR DATA [Sec. 614

helical scan. Alternatively, the antenna could be set to rotate uniformly
in azimuth, the elevation being manually controlled, or both azimuth and
elevation could be manually controlled. The performance at 10-cm
wavelength was more than adequate to give the 60,000-yd range desired
on single aircraft, and the convenience of having a common radar per¬
form both the search and the tracking functions is very great. Figure

Fig. 6-36.— LHTR transmitter-receiver-power-supply unit used in AN/APG-15 and other

sets.

6-37 shows an “x-ray” view of the SCR-581 with the antenna elevated into
operating position. For traveling, it is lowered within the trailer.

A conical scan is executed by the antenna of the SCR-584, the dipole
feed of the 6-ft paraboloid rotating rapidly about an axis which is that of
its mechanical, though not its electrical, symmetry. For precision track¬
ing, the azimuth and elevation error signals derived from this conical scan
are used, not to give an indication of pointing error, but actually to drive
servomechanisms which position the antenna mount. An error signal
in either coordinate wall cause the antenna to move in the direction neces¬
sary to reduce the error. This so-called “automatic angle tracking” was

Sec. 614] PRECISION TRACKING OF A SINGLE TARGET

209

embodied in the design because its precision of following is, unlike the
accuracy of manual tracking, not subject to human errors arising from
combat stresses and fatigue^ cri u ■> . - j

In order to ensure that the error signals are Pleasured with respect
to the desired radar echo only, and also to provide a continuous measure¬
ment of range, two type J displays are presented to the range operator
of the radar. These are circular range sweeps (Sec. 6-4) with radial
signal deflection. The coarse range scope shows all ranges out to a maxi¬
mum of 32,000 yd. and the fine scope shows a magnified trace of a 2000-yd

Fig. 6-37.—SCR-584 in operating position.

interval which can be chosen anywhere within the 32,000 yd. Markers
geared together at 1 to 16 and driven by the range handwheel are in front
of these tubes. When the marker on the 32,000-yd tube is put over the
signal echo to be tracked, the 2000-yd tube displays a range interval 1000
yd on either side of the target range. The marker on the 2000-yd tube
can then be set exactly on the leading edge of the target signal. When
this adjustment is made the marker is kept in register with the desired
signal, and continuous target-range information is sent to the computer.
Further, only those signals which come in a range interval of about 50 yd
immediately following the range for which the marker is set are sent to
the input of the angle-error measuring circuits.

210 THE GATHERING AND PRESENTATION OF RADAR DATA [Sec. 615

Circuits have been devised and tested which provide automatic track¬
ing in range, as well as in angle, but it appears that the judgment of the
range operator is of definite value in the operation of this equipment.
The operator is especially useful in following a desired target in the
presence of other near-by signals, which may be due to ground objects,
other aircraft, or “window” dropped to make radar tracking difficult
(Sec. 310).

The proving-ground accuracy of this set is about + 25 yd in range at
all ranges, and about +1 mil 1 or better in angle. With good radar
maintenance, this accuracy is achieved under field conditions. This was
one of the most widely used, versatile, and generally successful of all
allied wartime radar sets.

6-15. Precision Tracking During Rapid Scan. 2 —At the end of Sec.
6-12 we considered the design of systems for general air surveillance and
control w r hich offered fairly accurate information, renewed every few
seconds, on all the positional coordinates of all targets in the radar field
of view. This w'as claimed to be the operational ideal; and so it is, for a
radar set whose purpose is to permit the general control of aircraft. For
fire control, or for the close control of aircraft which is needed if a ground
controller is to coach a pilot through a blind landing approach, much more
precise and much more nearly continuous positional information than
that supplied by the V-beam is demanded.

The requirement of greater precision implies that narrower radar
beams must be used, and the requirement of more frequent information
implies an increase in the speed of scanning. These design changes, as
we have seen, seriously restrict the volume of space which can be covered
by the resulting radar set. However, the goal of maintaining at least a
partial situation picture by scanning, w r hile simultaneously providing
highly accurate positional information on a particular target being
tracked, is so attractive that several equipments have been designed to
attain it. The requirement of high scanning speed has led the designers
of all such sets to use “electrical” scanners (Chap. 9).

The design limitation on the volume of space that can be covered
frequently enough to be useful is least troublesome in the case of a radar
equipment designed to deal with surface targets. In this case, one is
interested only in coverage of a plane, not in searching the volume of
space that may contain aircraft. The most advanced equipment of the
rapid-scan precision-tracking type that was in field use at the end of
World War II w r as the AX/TPG-1, which had been designed for the
control of shore-battery fire against ships. For the purpose of fire control
against ships, a rapid-scan precision radar is most desirable, because the

1 A mil is a thousandth of a radian; thus 17.4 mils = 1°.

2 By L. X. Ridenour.

Sec. 6151 PRECISION TRACKING DURING RAPID SCAN

211

splashes of shells that miss the target can be seen on the scope of the radar.
Accurate “ spotting-in ” of fire both in range and in deflection is possible
with this type of set.

The antenna and scanning principle of the AN/TPG-1 (which was
also designated, in various modifications, as SCR-598, AN/MPG-1,
AN/FPG-1) are described in Sec. 9-14, and a perspective drawing of the
antenna is shown as Fig. 9-25. The radar beam produced was about
0.55° wide in azimuth; this narrow beam, coupled with the Msec pulse
length used, gave the set high resolution both in range and in azimuth.
A scope photograph showing the ability of the equipment to resolve
closely-spaced targets is shown as Fig. 6-38.

Fig. 6-38.—Row of small ships (LCI's in formation off Honolulu) shown on micro-B of
AN/TPG-1. Ships are less than 300 yd apart. (Reprinted from Electronics , December
1945.)

The AN/TPG-1 rapid scan covered a sector 10° wide centered on the
target of interest. The antenna could be mechanically rotated as a whole
to swing the center of this sector to any desired azimuth position, or could
be rotated continuously in azimuth during search. The set incorporated
a PPI which was useful when the antenna was rotating mechanically for
search. Its other indicators were a conventional type B presentation
which presented the 10° sector covered by the rapid scan, and a micro-B
indicator. The latter is normalized at 400 yd/in. At the ranges impor¬
tant in the operational use of this set, the distortion of the micro-B display
is very small. Electronic range and azimuth markers are provided on
the micro-B to aid in tracking. The azimuth error obtained in trials of
this set was less than 0.05 degrees.

The AN/MPN-1 equipment, often called GCA (for ground control of
approach), is the only radar designed during the war to provide accurate

212 THE GATHERING AND PRESENTATION OF RADAR DATA [Sec. 6 15

tracking on aircraft targets by means of rapid scanning. The inherent
difficulty of the problem is displayed by the fact that the GCA really
consists of three separate radar equipments. One is a PPI set which
presents a general picture of the air traffic situation; the other two, which
comprise the precision system, have “beavertail” beams narrow respec¬
tively in azimuth and in elevation. Each of these is rapidly scanned in
its narrow dimension, and separate indicators of the “stretched PPI”
type present the two angular coordinates. The set is fully described in
Sec. 8T3 of Vol. 2 of this series.

CHAPTER 7

THE EMPLOYMENT OF RADAR DATA

By B. V. Bowden, L. J. Haworth, L. N. Ridenour,

AND C. L. ZlMMERMANN 1

7-1. The Signal and Its Use.— The presentation of echo signals on an
indicator by no means completes the problem of designing an operation¬
ally useful radar system. It is necessary that action of some sort be
taken on the basis of the information afforded by the radar. To enable
this action to be taken promptly, intelligently, and correctly, an organiza¬
tion must be created. This organization begins with the radar indication
and extends to the execution of commands that arise from the situa¬
tion as displayed by the radar. The nature of these commands and the
nature of the organization that assimilates the radar data and gives the
commands differ widely from one functional use of radar to another.

The organization that employs radar data may be almost entirely
mechanized and automatic, as is, for example, the Army system for radar
antiaircraft fire control. In this system, the azimuth, elevation, and
range of a target are transmitted directly and continuously from the
radar to an electrical computer. The computer solves the fire-control
problem, determines the future position of the target, and transmits
azimuth, elevation, and range (fuze time) information to the guns of the
battery. The guns are positioned automatically by means of servo¬
mechanisms, and a fuze-setting mechanism is automatically adjusted to
cut fuzes to the time-setting indicated by the computer. 2 The duties of
the gun crew are the purely mechanical ones of supplying ammunition
and loading.

The Army system of antiaircraft fire control just sketched was out¬
standingly successful in the past war. This success can be viewed as
demonstrating the principle that, when a complicated task must be
carried out quickly and accurately under trying conditions, extreme
mechanization is well worth while, if it removes from human operators
the necessity for employing judgment and for performing complicated
operations. Such mechanization substitutes for the skill of operators the
design, manufacturing, and maintenance skills that are necessary to

1 Sections 7.1, 7.2, 7.4, 7.7, and 7.8 by L. N. Ridenour, Sec. 7.3 by L. J. Haworth,
Sec. 7.5 by B. V. Bowden, and Sec. 7.6 by C. L. Zimmermann.

* The use of proximity fuzes eliminates this step.

213

214

THE EMPLOYMENT OF RADAR DATA

[Sec. 7’2

supply and maintain the equipment required by mechanization. The
advantage of making this substitution is two-fold: the latter skills can
be applied under favorable conditions, while operator skill is required in
the field on the occasion of each crisis; further, there are usually many
more operators of a given equipment than there are designers, production
engineers, and maintenance men, combined. The total skill required is
thus more economically used under more favorable conditions if mech¬
anization is employed.

Most problems involving radar are far simpler than that of antiair¬
craft fire control. A simple set may be used on a ship, for example, for
navigation and collision avoidance. Under these circumstances, all that
is required is a good PPI display on the bridge, and perhaps an alarm
that gives a signal if a radar target approaches within a mile. Very good
navigation can be performed by comparing the PPI with a chart and
taking the range and bearing of sufficient identifiable points shown on the
radar to determine the location of the ship. The organization required
beyond the radar indicator consists in this case of very little more than
the ship’s navigator.

The problem of creating the most efficient organization for the use of
radar data, in each functional situation involving radar, is a very com¬
plicated one. During the war, it lacked the systematic study that its
importance and its complexity deserved. Since any treatment of system
design would be incomplete without some reference to this important
topic, this chapter will deal briefly with some of the devices and some of
the methods which have been worked out to translate into commands the
decisions taken on the basis of radar information. 1

It is to be emphasized that this subject is at least as difficult and as
important as that of the technical design of the radar itself, and far less
well understood. We can now build reliable radar equipment whose
principal performance limitation arises because the earth is round; the
major improvements to be looked for in the use of radar over the next
few years will lie, for the most part, not in the category of technical radar
design, but in the field of fitting the entire radar system, including its
operational organization, to the detailed needs of the use and the user.

EXTERNAL AIDS TO RADAR USE

7 - 2. Aids to Individual Navigation.—The most frequent and impor¬
tant use made of radar is as an aid to air and sea navigation. The
resemblance of the PPI display of a modern microwave radar set to a
chart is striking, and suggested very early that navigation would be
assisted by a device that enabled a map of the proper scale to be super-

1 The problem of devising an organization for using radar information in naviga¬
tion is discussed in Vol. 2 of the Series.

Sec. 7-2]

AIDS TO INDIVIDUAL NAVIGATION

215

posed on the radar indicator. Figure 71 is a schematic diagram of one
method of accomplishing this. The indicator screen is viewed through
an inclined, partially reflecting piece of glass which reflects to the eye
of the observer the image of a screen on which a chart is projected.

Special coatings for glass have been developed which give a high
reflectivity in the blue region of the spectrum, while transmitting yellow
light substantially without loss. If such a coating is used on the inclined
mirror, the yellow persistent signals on the PPI tube can be seen with
nearly .their full intensity, while the chart image can be projected on the
mirror in blue, so that it is reflected with little loss in intensity.

If a radar fitted with such a
device is being used for the navi¬
gation of a moving ship or aircraft,
the charts used for projection must
be adjustable and easily changed.

Methods have been worked out for
storing a large amount of map
information in a small space by
the use of microfilm, and for pro¬
viding motion of the chart in
the projector. The direction and
speed of this chart motion can be
adjusted by the operator so that
the chart and the radar display
stay in register as the vessel
moves; when this has been accom¬
plished the direction and speed of the ship, as well as its instantaneous
position, are known.

Few such chart-projection devices have been built. They are com¬
plicated, bulky, and expensive, and the function they perform can rather
simply be done by other means.

Dead-reckoning Computers. —The direct comparison of the PPI with
an appropriate chart is an unnecessary elegance if it is desired merely to
take occasional fixes and to proceed between fixes by the usual methods
of dead reckoning. This is, in any event, the only safe means of naviga¬
tion. When the first microwave PPI radar was installed in aircraft,
careless navigators neglected their dead reckoning in the belief that the
radar would enable them to determine their position whenever necessary.
This procedure resulted in getting lost with such regularity that radar
was soon established as an adjunct to dead reckoning, rather than a sub¬
stitute for it.

To assist in dead reckoning, particularly in aircraft navigation where
high speed and frequent course changes make it difficult, various forms

Fig. 7*1.—Schematic diagram of chart
proj ector.

216

THE EMPLOYMENT OF RADAR DATA

[Sec. 7-2

of dead-reckoning computers, or odographs, have been developed. The
control box of one such computer is shown in Fig. 7-2. This device,
developed in the Division 17 program of the NDRC, receives information
from a true-airspeed meter and a repeater compass. These data are
resolved into cartesian velocity components along the north-south and
east-west directions, and these velocity values are integrated to provide
continuous readings of air position with reference to any chosen point of
departure.

A mechanism is also provided to indicate ground position by taking
account of the effect of wind. The direction and speed of the wind (as
determined from double drift readings, meteorological information, com¬
parison of earlier wind settings with the actual course made good, radar
fixes, or otherwise) can be set into the device by means of knobs shown

in Fig. 7-2. Wind velocity is re¬
solved into components along the
north-south and east-west direc¬
tions, integrated, and. the result
added to the air position to give
the ground position with respect
to the point of departure.

Air position and actual ground
position both appear on the
counter dials shown at the lower
left. The output signals of the
unit can also be used to actuate
a plotting arm which moves over
a map table not shown in Fig.
7-2. With this addition, the de¬
vice draws on a map the actual
ground track made good by the aircraft carrying the instrument. Vari¬
ous map scales can be selected fpr the plotting table by means of a knob
on the control box. The control box can also be provided with a gear
train that actuates a mechanism showing latitude and longitude directly,
in addition to showing the departure from the last fix. In a carefully
made installation, the cumulative error of this instrument amounts to
only i per cent of the total distance traveled from the point of departure.

Ground-position Indicator, GPI .—Although the device just described
aids in performing dead reckoning, and to this extent assists in radar
navigation, it is convenient to present the results of the dead reckoning
directly on the radar scope. This has been done in a device called the
“Ground-position Indicator,” or GPI.

The GPI provides an electronic index for the PPI tube of the radar
in the form of the intersection of a circle of constant range and an azimuth

te,...-... ..j

Fig. 7-2.—Control box of aircraft odograph
or dead-reckoning computer.

Sec. 7-2]

AIDS TO INDIVIDUAL NAVIGATION

217

marker. Once this index has been set on a radar echo by means of
adjusting knobs provided on the device, the index will move across the
face of the tube with the echo, provided that the wind setting has been
made properly, regardless of maneuvers of the aircraft.

A simplified schematic diagram of the GPI is shown in Fig. 7-3. To
the left of the box marked “Rectangular to polar coordinate resolver,”
the device is identical with the dead-reckoning computer just described.
Since the basic coordinates of the PPI are range and azimuth, it is neces¬
sary to convert the cartesian position information to polar coordinates;
this is done in the resolver shown. The azimuth resulting from this
operation is compared with the instantaneous azimuth of the radar

Fig. 7-3. —Simplified schematic diagram of Ground Position Indicator.

scanner. When the two are equal, an azimuth mark is put on the radar
indicator electronically.

The range information provided by the resolver is measured hori¬
zontally along the ground; it must be corrected for the altitude of the
aircraft if, as is usual, slant range is displayed by. the radar indicator.
This is done by means of the electrical triangle-solver labeled “Slant range
circuit,” into which the value of aircraft altitude is set by the operator.
The value of slant range computed by this device is used to put a range
marker on the PPI at the appropriate distance from the origin of the
sweep.

Taking a fix with the GPI involves turning the N-S and E-W fix knobs
until the intersection of the range and azimuth marks appears on top of
an identified target signal. The “fix” dials will then read the ground
range of the target from the aircraft, resolved into north-south and east-
west components. As the aircraft moves, these dials will continue to
read the correct position of the target relative to the aircraft and the

218

THE EMPLOYMENT OF RADAR DATA

[Sec. 7-3

index will continue to stay on the target echo, provided that the correct
value of wind has been set into the device by means of the two “wind”
knobs shown. Even after the index and the target echo have moved off
the face of the radar indicator, the dials will still show the target position
relative to the aircraft.

The determination of wind requires that two fix operations like that
just described be made on the same echo (which need not correspond to a
target whose identity is known). The major correction which will have
to be made at the second fix is that arising from the effect of wind. The
wind and fix knobs of the GPI are arranged so that they can be gripped
together and turned together by the same amount. A proper choice of
scale factors will enable the operation of taking the second fix to correct
the wind velocity at the same time. If the wind error is to be taken out
exactly by this process of double-gripping the wind and fix knobs, account
must be taken of the fact that the proper ratio between the scale factors
of these two knobs is a function of the time elapsed since the first fix was
made. The GPI is arranged with a ratio of scale factors which changes
with time in the proper way, so that double-gripping will remove wind
errors entirely at the second fix, providing this second fix is made at any

time up to six minutes after the
first.

7-3. Aids to Plotting and Con¬
trol.—The problem of controlling
aircraft on the basis of radar infor¬
mation involves careful plotting of
the signals seen on an indicator.
The controller desires to know the
position of a given signal with
respect to a map or grid—which
must therefore be somehow super¬
posed on the display—and he
wishes to record the position of a
target on successive sw'eeps, to determine the direction and approximate
speed of its motion.

Optical Superposition .—Optical devices of the same general character
as the chart projector mentioned in the last section are helpful for these
purposes. Two schemes involving the use of a partially reflecting mirror
to place a virtual image of a screen in optical superposition with the dis¬
play are illustrated in Figs. 7 4 and 7 5.

The device of Fig. 7-4 is identical in principle with the chart projector
shown as Fig. 7-1. The virtual image formed in this case, however, is
that of an edge-lighted screen which can be engraved with a scale or a set
of indices. Multiple sets of indices with different scale factors can be,

Nonreflecting surface

10 to 20 % reflection

g Edge-lighted
scale

Fig. 7-4. —Method of superimposing an edge-
lighted scale on a CRT pattern.

Sec. 7-31

AIDS TO PLOTTING AND CONTROL

219

conveniently provided by ruling each individual set on a thin transparent
sheet. The sheets are then stacked and arranged to be edge-lighted
individually; thus only the chosen scale appears. Such multiple scales
are used on the indicator of the V-beam height-finding display described
in Sec. 6T2, to permit the use of range sweeps of various lengths.

The arrangement of Fig. 7-5 permits the use of only one scale, but
affords, as shown, the considerable advantage that a wax pencil can be
used for plotting the position of each radar echo of interest, with a mini¬
mum of difficulty from parallax. As the pencil point touches the edge-
lighted plotting surface, it glows brightly over the small area of contact,
and small corrections in the position of the point can be made before a
mark is actually applied to the screen. Although the operator must look
through the screen itself at its
virtual image below, the real and
virtual images can be distin¬
guished, providing the scales are
not too complex, by their positions
and usually by a difference in in¬
tensity or appearance.

Display Projection .—An out¬
standing problem in the use of
radar for control is that of trans¬
ferring radar plots from the face of
a small indicator tube to a large
board where plotting can be done,
other information entered, and a
display visible to many people in
a large room presented. This
problem has been approached in
several different ways. One—that of telling grid coordinates of a target
to plotters who enter the target position on a large board—will be described
in Secs. 7-5 and 7-6. Another, which seems obvious but presents con¬
siderable technical difficulty, is that of direct optical projection of an
enlarged real image of the display on an appropriate screen.

The light intensity from a persistent cathode-ray-tube screen of the
usual type is too low for satisfactory enlarged projection. Several alter¬
native methods of accomplishing the same result have been used or
proposed, including:

1. Splitting the cascade screen (Sec. 13-2) into two parts, the blue
component being in the tube and the persistent component on the
projection screen. Although this scheme is better than direct
projection of a cascade screen, results are far from satisfactory.

Fig. 7-5.—Method of plotting with the aid of
optical superposition.

220 THE EMPLOYMENT OF RADAR DATA [Sec. 7-3

Further, the screen must be well shielded from stray light if this
method is to be used, and this somewhat limits its usefulness.

2. Televising the persistent screen and using the video signals so
obtained to modulate a high-intensity short-persistence tube suit¬
able for projection. The results obtained with this rather com¬
plicated scheme up to the end of the war were mediocre.

3. Storing the radar picture on an image orthicon or other storage
device which can be rapidly scanned electrically to produce tele¬
vision signals. This method, although not well developed at the
end of the war, holds great future promise.

4. Use of a dark-trace tube, or “skiatron.”

5. Rapid photographic projection.

The last two methods mentioned are the only ones developed fully
enough during the war to warrant further description.

The Skiatron .—The dark-trace tube, described briefly in Sec. 13-2,
has been used as the basis for a reasonably successful projection system
both in England and in America, the principal differences being in the
optical systems used. In England, an extremely flat-faced tube serves
as the source for a wide-aperture lens system; in this country a tube has
been designed to fit a Schmidt optical system.

Figure 7-6 illustrates the latter. The cathode-rav tube, whose face
is precisely spherical, is mounted with this face concentric with the
spherical mirror of the optical system. Light from an intense mercury-
arc or tungsten source is concentrated on the tube face by the lens-and-
mirror arrangement shown. The geometry is so chosen that the Schmidt
correcting plate comes roughly at the neck of the cathode-ray tube. A
45° mirror reflects the light to a horizontal projection screen which forms
part of the top of the cabinet housing the equipment.

Sec. 7-3]

AIDS TO PLOTTING AND CONTROL

221

The display is formed as in any other cathode-ray tube, except that it
is necessary to minimize the diameter of the focusing and deflection coils
to prevent them from cutting off too much light. Between 10 and 12 kv
is applied to the final anode of the tube.

Signals appear as magenta-colored patches against a white back¬
ground, and they can be viewed in the presence of a reasonably high level
of ambient light. This property, together with the large, flat, parallax-
free image, makes the display extremely useful for measurement and
plotting. However, it has serious inadequacies which arise from short¬
comings of the skiatron tube. Contrast is always low, particularly at
low duty ratios. Repeated signals have a very objectionable tendency
to “bum in,” becoming stronger than transient signals and remaining on
the tube long after the radar echo that created them has moved away or
disappeared. This difficulty can be considerably alleviated by occa¬
sionally raising the tube temperature and scanning the screen with a weak
electron beam, both of which measures tend to bleach the screen. A
fairly intense bumed-in pattern can thus be removed in one or two
minutes.

In its present technical state, the skiatron is most useful for observing
and plotting the courses of ships, from either a shipboard or a coastal
station. It is less satisfactory when used to display aircraft signals,
because of the poor contrast in their more rapidly moving echoes.

Rapid Photographic Projection .—The inadequacies of other methods
of providing a large projection display of a radar indicator led to the
development, by the Eastman Kodak Company, of means for the
photography of one full 360° sweep of a PPI, rapid photographic process¬
ing of the exposed film, and immediate projection of the developed pic¬
ture. The equipment is shown in Fig. 7-7.

The camera uses 16-mm film, of yhich 350 ft are required for con¬
tinuous 24-hr operation at two scans per minute. An instantaneous blue
phosphor serves best for photographing. After exposure to a full scan,
each frame is processed with metered quantities of developer and fixer,
the total processing time being 13-5 sec. A total quantity of less than a
gallon of the two solutions is required for 24-hr operation. The projector
unit consists of a 300-watt lamp and a simple optical system. The film
is cooled by an air blast during projection. The maximum diameter of
the projected image is 8 ft, and images of a given point can be repeated on
successive frames within a circle of 1-in. diameter at this magnification.

Plotting means employing this device were just being worked out at
the end of the war. 1 It appeared that this was a highly effective and
satisfactory method of large-scale direct presentation of a radar display.

1 L. L. Blackmer, “P 4 I (Photographic Projection PPI),” RL Report No. 725,
April 26, 1945.

Record film

Blower

- Waste
chemicals

Pressure

chamber

Vacuum

pump

Flo. 7-7 -Rapid photographic PPI projectur.

indicator

Developer

Camera and processing

Projection lamp

THE EMPLOYMENT OF RADAR DATA

[Sec. 7-3

Sec. 7-3]

AIDS TO PLOTTING AND CONTROL

223

Video Mapping .—None of the methods so far described permits the
superposition of an “electronic” map on the display. By this term is
meant the addition to the radar signals of signals which, by appropriate
intensity-modulation of the indicator, reproduce on the display itself a
map, a grid, or any pattern that may be desired. The position of radar
echo signals can be compared with this electronic map with complete
freedom from parallax, and, in addition, any distortions or imperfections
of the display affect the grid and the signals equally and thus produce no
reading error. A very satisfactory method of accomplishing this has
been given the name of “video mapping.”

The signals required to produce the desired modulation are derived
from the device illustrated in Fig. 7-8. The desired map, in the form of
opaque lines on a transparent
background or vice versa, is placed
immediately in front of an auxil¬
iary PPI of the highest precision
obtainable. This PPI rotates in
synchronism with the radar an¬
tenna and executes its range sweep
in the proper time relation with
the radar transmitter, but operates
at a constant intensity, receiving
no video signals. The cathode-
ray tube used has a short-persist¬
ence blue screen; the intensity is
adjusted to a medium or low level.

As the moving spot of the auxiliary
PPI moves behind the map to be
reproduced, a photocell placed two

Fig. 7-8.—Video mapping transmitter.
The aperture in front of the phototube ia
small enough so that the parallax between the
spot on the CRT screen and the marks on the
plotting surface is small.

or three feet from the map receives a signal whenever the rays from the
spot to the photocell undergo a change in absorption. Because of the
rapid motion of the spot in its range sweep, these signals are in the video¬
frequency range. The fast screen avoids any appreciable “tailing” of
signals.

The signals from the photocell are amplified and mixed with the radar
echo signals with a polarity such that on the final display the lines of the
map are brighter than the background. In the absence of limiting,
gradations of light and shadow can be presented. Figure 7-9 is a repro¬
duction obtained on a second PPI tube of a photographic negative used
as a subject for video-mapping transmission. Figure G.8 was also pro¬
duced by video mapping, the final display being a B-scope.

This method has the very great advantage that the map is correctly
correlated with the radar display regardless of the degree of off-centering,

224

THE EMPLOYMENT OF RADAR DATA

[Sec. 7-3

Sec. 7-4]

THE RELAY OF RADAR DISPLAYS

225

or of any deliberate or accidental deformation or distortion. The
accuracy is determined entirely by the precision of the scanning PPI and
by the geometrical relationship between the PPI and the map. Slight
changes in parallax between the center and the edge of the tube can be
compensated by using a suitably nonlinear range sweep.

If the radar site is moving, a compensating motion must be applied
to the map in order to maintain the proper relationship on the final
displays.

This method can be applied to any type of index or marker, and has
obvious uses as a substitute for elaborate computing circuits under some
circumstances.

7-4. The Relay of Radar Displays. —It is common for the best location
of the radar station and the optimum location of a control center to be
different. The radar site is chosen from the standpoint of good coverage,
freedom fiom permanent echoes, and the like; the criteria entering into
the choice of site for a control center are usually entirely different. Also,
a control center should receive supplementary information from other
radar installations located elsewhere, even though a single radar equip¬
ment may provide the primary data for control of operations. This will
enable the coverage of the primary radar to be supplemented by informa¬
tion from neighboring sectors, and will provide coverage of possible
“blind spots” of the primary radar.

The telling of plots by telephone land line was the technique first used
(Sec. 7-5) for the transmission of radar data from one point to another.
Substantial errors and delays are inherent in this procedure. Far more
important, when the information to be transmitted has been gathered
by a modem long-range, high-definition radar, is the low traffic-handling
capacity of the system of telling and plotting. Literally hundreds of
targets may show at a given time on the indicator of such a radar as the
first one described in Chap. 15; an attempt to convey with adequate
accuracy and speed the information provided at a rate of four sweeps per
minute is hopeless under such conditions.

Considerations such as these led to the development of means for
reproducing radar displays at a distant point by transmitting the radar
video signals and appropriate synchronizing information by more or less
conventional radio practice. The technical problems of “ radar-relay, ”
as this is called, have been worked out, and systems for the purpose are
discussed in detail in Chap. 17.

Radar relay is mentioned here to emphasize its usefulness as one
element in the creation of an organization for the use of radar data. An
example of an operational system in which this technique is important
is given in Sec. 7-8.

226

THE EMPLOYMENT OF RADAR DATA

[Sec. 7-5

EXAMPLES OF RADAR ORGANIZATIONS

In the following sections are given very brief sketches of a few
radar organizations with which some experience has been obtained. The
systems described are, for the most part, necessarily those set up in war¬
time for the purposes of war, and to this extent do not represent useful
models for peacetime radar organizations. It will, however, be instruc¬
tive to consider briefly a few typical systems.

7-6. Radar in the RAF Fighter Command. —Just as the first radar
equipment to be used in operations was that installed for the air defense
of the British Isles, so the first operating radar organization was that of
RAF Fighter Command, the user of this equipment. When the organi¬
zation was fully developed, the number of people involved in the inter¬
pretation of the radar information and in making use of it was comparable
to the number required to obtain it.

Organization of the Home Chain .—It has been mentioned in Sec. 6 -9
that the performance of CH stations depended very much on the nature
of their sites. Moreover, owing to a shortage of trained men and to the
difficulties involved in maintaining equipment of this kind in wartime,
the antenna systems were often badly installed and inadequately main¬
tained. In consequence, large errors in apparent azimuth were very
common; most stations had errors of 10° or 15°, and errors as large as 30°
were not unknown. The method of measuring height depended on
reflection of the received waves from the ground, and almost invariably
the height calibration of a station was different along different azimuths.
Each station had to be checked and calibrated both for height and azi¬
muth by an elaborate and difficult series of test flights.

The complicated nature of the corrections necessary on each aircraft
plot, and the requirement for speed and accuracy in applying these cor¬
rections, led the British to design and install what is perhaps the first
device intended for assistance in the use of radar data, as opposed to the
gathering and display of that data. This is the celebrated “fruit
machine,” 1 a complicated calculating machine made up of standard
telephone selector switches and relays. The operator measured the
range of the target by setting a marker to the echo on the A-scope. She
then turned the goniometer until the echo disappeared, and pressed
buttons transmitting range and apparent azimuth to the fruit machine.
The machine automatically applied the appropriate correction and
deduced the true azimuth, multiplied the target range by the sine and
the cosine of this true azimuth, added in the rectangular map coordinates
of the station itself, and deduced the coordinates of the target. This

1 It was named after the English equivalent of the American slot machine used for

gambling.

Sec. 7-51

RADAR IN THE RAF FIGHTER COMMAND

227

information was displayed in lights to a “teller,” who passed the infor¬
mation over a telephone line to Fighter Command Headquarters. At a
later stage, the plots were passed by teletype to save time. The whole
computation process was completed in a second or so.

The operator then pressed a button which connected the goniometer
to the height-finding antenna arrays. Again she turned the goniometer
until the signal disappeared, and pressed a button. The height of the
target was computed by the fruit machine and passed to headquarters.

Radar plots from all of the Chain stations were sent to Fighter Com¬
mand in Stanmore, north of London. Because of the shortcomings of the
early radar equipment, and the “blind spots” in the coverage of indi¬
vidual sets, it was felt to be essential to combine the information from
all radar stations at a central point. This was done at a so-called
“filter center.”

In a large underground bombproof room was mounted a central
table whose surface was a gridded map of England. A crew of plotters,
each with a telephone connection to one of the radar stations, stood
around the table at positions corresponding to the geographical locations
of the Chain stations. As a plotter received plots over the telephone,
she put colored disk markers in the grid positions indicated. It usually
happened that two or more stations were simultaneously plotting the
same aircraft, so that several girls might be putting down counters repre¬
senting the same formation. Owing to the errors in the system and the
variable delays in the plotting process, the interpretation of the piles of
disks in terms of aircraft was not easy. Special officers known as filterers
stood beside the girls and decided, for example, whether two adjacent
tracks were really separate, or represented the same aircraft, erroneously
plotted by one of the stations. After he had analyzed the data, the
filterer put on the map a little plaque that bore his best estimate of the
identity, position, height, speed, and number of aircraft in the formation.

This whole process was observed by filter officers who sat on a balcony
overlooking the map. They were informed of the plans for the move¬
ments of friendly aircraft. They were able to direct the operations of the
whole Chain and to decide which formations should be plotted by each
station. The work of the filter officer called for a considerable under¬
standing of the performance of CH stations, and an appreciation of the
good and bad qualities of each individual installation.

Established tracks on the filter-room board were telephoned by a
teller to a second plotting board maintained in an “operations room.”
Here the filtered radar tracks were combined with plots of the Observer
Corps (visual airplane spotters), and with fixes made by means of radio
direction finders. In this main control room, the aim was to display the
whole of the picture of the air war; all operations were generally directed

228

THE EMPLOYMENT OF RADAR DATA

[Sec. 7-5

from this point. The detailed control of fighter interceptors was carried
out from group and sector headquarters, where plots were maintained on
the basis of information repeated from Fighter Command Headquarters.

The operation of this system was much more difficult than might be
inferred from this brief description. If the CH stations had been perfect,
it would still have been difficult to interpret some hundreds of plots every
minute, all subject to variable delays and to the personal errors of the
observers. Quite trivial difficulties proved surprisingly hard to over¬
come. It was hard to find room for all the plotters around the table.
They could not plot fast enough. They might disturb one set of plots
when they leaned over to plot another aircraft. Such rather simple
difficulties could be, and often were, the limiting factors on the use that
could be made of the radar plots, and an intensive study of all the stages
in plotting and filtering was made throughout the early years of the
war.

Despite the large number of people necessary to this system, and its
prodigal use of telephone land lines for the telling of plots, its operational
limitations were severe. Under conditions of moderate aircraft density,
a good filter officer with a good organization could filter plots with an
accuracy of perhaps 70 per cent. When plots were sparse, the accuracy
was excellent, and the only objection to the system was its unavoidable
time lag in reporting. Under conditions of high aircraft density, the
system broke down, and it was commonplace to cease reporting in certain
areas where the density was so high that filtering was impossible.

In spite of these handicaps, very considerable success attended the
use of this system in the Battle of Britain and thereafter. A tendency
grew to forget that the main reason for organizing the reporting and con¬
trol system in this centralized way was that a single radar could not be
relied on to give a sufficiently complete or accurate picture of events
in the air. The great technical improvements of 1943 and early 1944
resulted in long-range, high-definition microwave radar having good
coverage if properly sited. This* improved equipment made it possible
to depend on a single radar installation for a substantially complete
picture of the air situation.

Delays and errors unavoidable in a complicated scheme of telling and
plotting are largely eliminated in a system that combines the operational
organization with the radar equipment. Controllers who give instruc¬
tions to aircraft are able to work directly from the radar display and
therefore have a far more accurate and up-to-date appreciation of the
situation than can be obtained from a plot, however well maintained it
may be. This was eventually appreciated, and such systems have been
put into very successful operation. Such a system is described in the
following section.

Sec. 7-6]

THE U.S. TACTICAL AIR COMMANDS

229

7'6. The U.S. Tactical Air Commands. —Each U.S. Army that
fought in Europe was accompanied by a Tactical Air Command whose
mission was that of providing air defense in the forward sector occupied
by the Army concerned, of conducting offensive operations against enemy
ground troops and installations in the immediate tactical area, and of
conducting offensive operations in close cooperation with friendly ground
units. The aircraft of a Tactical Air Command, or TAC, were almost
entirely fighters and fighter-bombers. Each TAC went into the fighting
on the Continent with a radar organization of the general character shown

Ground observer posts Ground observer posts Ground observer posts
Fig. 7-10.— Fighter control system of IX Tactical Air Command.

in Fig. 7T0, which displays the setup of the 555th Signal Air Warning
Battalion attached to IX TAC (which operated in support of the Ameri¬
can First Army).

Each of the three Forward Director Posts (FDP’s) had operating
with it five Ground Observation Posts (GOP’s). Men placed far forward
observed air activity that might consist of low-flying hostile craft not
covered by the radar placed farther back of the front lines. Each GOP
reported by radio telephone to a Net Control Station common to the
group of five. The NCS then phoned pertinent information to the FDP;
an alternate NCS was mainted for use in emergencies.

The radar of the TAC was mainly deployed at the FDP’s. These
sites were charged with reporting air activity to the Fighter Control
Center, which was located at the forward headquarters of the TAC,

230

THE EMPLOYMENT OF RADAR DATA

[Sec. 7-6

usually occupied jointly with Army forward headquarters. In addition,
they executed direct control of airborne fighters on certain types of
missions.

Let us consider first the reporting function of the FDP, leaving until
later the consideration of control directly from the FDP. The following
steps must occur before radar information is in the form in which it was
used for decision and action:

1. The coordinates of a target signal are read off the display at the
radar station.

2. A number is assigned to this particular track, on which continuous
plotting will be maintained.

3. An attempt is made to identify the track from the following data:

a. Known location of friendly aircraft.

b. Response to IFF interrogation (Chap. 8).

c. Intelligence information on enemy tracks.

4. A series of symbols is telephoned to the FCC, giving the following
information:

a. Identification of track as friendly, enemy, or unknown.

b. Number assigned to track.

c. Location of plot.

d. Estimated number of aircraft.

e. Height.

/. Direction of flight.

At the FCC the following steps take place:

1. The filter officer must determine whether the plot is a continuation
of an old track or the beginning of a new one.

2. The track is reidentified, if possible, from the fuller intelligence
information available at the FCC.

3. Plots reported from more then one radar station must be recog¬
nized as belonging either to the same track or to different tracks.

4. Cards bearing the information listed under (4) of the preceding
paragraph are put into a marker called a “Christmas tree.”

5. The Christmas tree is moved on to a large plotting board to occupy
the position reported for the track.

All of the steps just described require time, and the large plotting
board at the FCC is usually between three and five minutes behind the
existing air situation. Although this means that the aircraft positions
displayed are wrong by some 20 or 30 miles, the delay is usually tolerable
for air-warning purposes.

In the “sector control” that is executed by the FCC, aircraft con¬
trollers observe the relative positions of tracks on the large plotting board

Sec. 7-6]

THE V.S. TACTICAL AIR COMMANDS

231

and issue radiotelephone instructions to friendly fighters in an effort to
bring them into favorable positions to counter air attacks. For defensive
operations, this sort of control is usually adequate; enemy air attacks will
ordinarily be directed at one of a few vital areas where substantial damage
can be done. Even with his five-minute-old information, the controller
can make a shrewd guess as to the target of such an attack, and can
marshal defensive fighters accordingly. For many types of mission
however, direct control from the FDP’s is required.

Reporting Capabilities of FDP’s .—Between Oct. 21 and Nov. 16, 1944,
a study was made by the Operations Analysis Section of Ninth Air Force
of the reporting work done by the three FDP’s of IX TAC. Because of
the difference in the amount and character of air activity by day and by
night, daily and nightly averages were separately computed for the
following data: the average number of separate plots per track reported,
the average track duration in minutes, and the average number of plots
per height reported. The results are shown in Table 7T.

Table 7 1. —Reporting by FDP’s of IX TAC, 21 October to 16 November 1944

232

THE EMPLOYMENT OF RADAR DATA

[Sec. 7-6

50 per cent of the total plots obtained were passed on. However, 84 per
cent of the tracks were reported, the difference being due to single-plot
tracks which were not reported. The average number of plots per track
was 6.2 and the average track duration 9.5 min. Hence, on the average,
a plot was obtained on each track once every 1.8 min , which is considered
to be fairly continuous tracking.

Close Control by the FDP .—At the turn of the year 1940^41, the
Luftwaffe abandoned its daytime attacks on England and turned to night
bombing, the attacking aircraft operating individually. This led to the
development by the British of an elaborate system of nightfighter defense
which has been described elsewhere. 1 One of the features of this system
was exact control of the nightfighter, prior to his interception of the hostile
bomber, by a ground controller at a GCI (for Ground-controlled Inter¬
ception) radar station. The aim of this control was to put the night-
fighter behind, a little below, and on the same course as the hostile
aircraft, in which position he was well situated to complete the inter¬
ception with the help of airborne radar equipment he himself carried.

By 1943, both this GCI technique, involving precise control of single
aircraft by a controller located at a radar station, and the daytime sector-
control technique described in Sec. 7-5, involving the control of formations
of fighter interceptors from a central station at which radar data were
assembled and assessed, were firmly established procedures. In that
year two things happened which gave rise to the technique of close con¬
trol as it was practiced by the FDP’s of the American TAC’s in the
Continental phase of the European war. A young American officer, who
was working with the RAF as a member of the Electronics Training
Group sent to the United Kingdom soon after the L’nited States went to
war, conceived the idea of controlling formations of day fighters directly
from the information available at his radar station alone. Meanwhile
battle experience in Africa showed that an independent radar set could
pass to airborne fighters useful information on the disposition of enemy
aircraft.

The American officer’s novel idea did not gain immediate acceptance
since control of several squadrons of fighters in daylight requires tech¬
niques quite different from those of the GCI control of a single night-
fighter. Finally, the officer was given permission by the late Air Chief
Marshal Sir Trafford Leigh-Mallory to control wings of fighters directly
from his radar station, entirely independently of the sector-control
system.

While the new technique was being worked out and the confidence of
pilots and controllers was being developed, 15 RAF planes were lost for

'Sec, for example, "Radar (A Report on Science at War),” Superintendent of
Documents, U.S. Government Printing Office, Washington, D.C., Aug. 15, 1945.

Sec. 7-6]

THE U.S. TACTICAL AIR COMMANDS

233

10 enemy planes downed. After this initial shakedown period, 90 enemy
planes were destroyed for a loss of 13 to the RAF, before enemy jamming
of the 1.5-m equipment used in this first work put an end to its usefulness.

The success of this experiment led the British to design a higher-
frequency radar specifically for the purpose of close control, and resulted
in the modification of the first of the American 10-cm sets, on its arrival
in England, to fit it for similar close control. Because of the African
experience the control setup was made mobile. Figure 7T1 shows the

and briefing

Fig. 7-11.—Layout of radar control center.

arrangement of facilities arrived at for an installation designed for use in
close control.

The antenna is shown mounted on a low structural-steel tower. For
mobile operation the antenna is mounted on a trailer (see Fig. 9T5).
Power is supplied by diesel-electric units housed either in a Jamesway
shelter, as shown, or in trailers. The maintenance shelter contains, in
addition to workbenches, spares, and test equipment, the power control
unit for the set. Another shelter houses a number of B-scopes used for
reporting signals to the operations shelter, where they are plotted. The
coverage of each B-scope can be chosen to give the best total coverage of
the area important to the operations being carried on by the station.
Another shelter houses the telephone switchboards, a triangulation table

234 THE EMPLOYMENT OF RADAR DATA [Sec. 7 G

Fig. 7-12.—Interior of operations shelter.

for making radio direction-finder fixes, an office for the senior controller,
and a briefing room for controllers.

The operations shelter is the heart of the system. Its interior is
shown in more detail in Fig. 712. On a dais at the rear of the shelter sit
the chief controller, who is responsible for the general operation of the
station, and officers concerned with identification of tracks, liaison with
antiaircraft artillery, Army, and Navy (as required), and other coordina-

Sec. 7-6]

THE U.S. TACTICAL AIR COMMANDS

235

tion functions. Off-center PPI scopes are provided for the chief con¬
troller and the deputy controllers, the latter sitting along the sides of the
shelter. At the right of the shelter, near the plotting board, sits the
supervisor, who is responsible for the technical operation of the radar set.
He has a console patchboard by which he can communicate with any of
the operators, maintenance men, tellers, or plotters. In front of the
plotting board is a filter officer who decides which plots are to be told to
the FCC.

The large vertical plotting board is shown in more detail in Fig. 7T3.
It is made of transparent plastic and is edge-lighted, so that plots put on

in grease pencil by plotters working behind the board appear brilliantly
illuminated when viewed from the front. Each plotter is connected by
telephone with a teller who is watching a B-scope in the reporting shelter.
Auxiliary boards to the right and left of the main plotting board give
pertinent information on such things as the heights reported (by an
auxiliary radar height-finder) for various tracks, weather and winds aloft,
radio-frequency channels in use for communications and for direction¬
finding, and the ready status of aircraft at various fields.

The deputy controllers, each of whom is charged with giving instruc¬
tions to a certain formation as directed by the chief controller, depend on
the plotting board for their general picture of the air situation, and work
directly from their PPI scopes to determine the instructions to be given

236

THE EMPLOYMENT OF RADAR DATA

[Sec. 7-6

Sec. 7 6]

THE U.S. TACTICAL AIR COMMANDS

237

Iiti. 7-15. FDP of U.S. Tactical Air Command, France. March 1945.

238

THE EMPLOYMENT OF RADAR DATA

[Sec:. 7-7

saw service in the European war, but it is based soundly on months of
combat experience with improvised and frequently changed systems and
devices. An actual FDP using one of the preproduction sets is shown
in position in eastern France in Fig. 7-15. The central antenna is that of
the main radar; the two that flank it are those of British Type 13
heightfinders (Sec. 6-12). The system is largely mounted in and operated
from trucks, and it can all be taken down, loaded on trucks, unloaded
at a new site, and erected and put back on the air in a total time of less
than 24 hr.

7-7. Close Control with SCR-584. —Figure 7T0 shows, attached to
the FDP’s, SCR-584 radar sets. This equipment, designed for accurate
tracking of a single aircraft at a time, in order to permit antiaircraft fire
control, can also be used to provide to a ground controller the information
necessary for highly precise control of the aircraft being tracked. It was
so used by the TAC’s in Europe.

Since the information on target position is normally transmitted to
the antiaircraft computer by means of synchros or accurate potentiom¬
eters (Sec. 13-4), it is necessary to provide a supplementary method of
displaying target position t6 enable the set to be used for ground control.
This was first done by means of the 180° plotting board shown in use in
Fig. 7T6. An arm, pivoted beneath the surface of the board on the side
nearest the controller, swings in azimuth in accordance with the orienta¬
tion of the radar antenna. Range information from the set is used to
control the position of a range carriage that runs in and out along the
azimuth arm. The carriage has an optical system which projects a small
spot of light up through the glass surface of the plotting board. Over the
surface of the plotting board is stretched a map of the area surrounding
the radar set, carefully adjusted so that the point on the map occupied by
the radar is directly above the pivot of the moving arm. The scale factor
of the range-carriage mechanism is adjusted to correspond with the scale
of the map being used, which may be either 1 to 50,000 or 1 to 100,000.
When the radar is tracking a target, the spot of light from the range car¬
riage shows up on the map just at the position over which the airplane
is flying at that moment.

The controller can thus issue his instructions w T ith full and constant
knowledge of the exact position of the aircraft under his control. This is
to be contrasted with the situation that obtains in ground control from a
scanning radar; in that case the controller has only one “look” at his
target per scan—that is, perhaps once in 15 sec. However, he sees all
other targets in the air within range of his radar. The controller in the
SCR-584 sees the position of his aircraft continuously, and in proper
relation to the terrain, but the price paid for this is that he has no knowl¬
edge of the whereabouts of other aircraft.

Sec. 77]

CLOSE CONTROL WITH SCR -584

239

Figure 7-16 also gives an idea of the compact operational organization
of a control SCR-584. Range and PPI operators sit at the radar panels,
behind the controller. The controller works alone, in full charge of the
operation once an aircraft or a flight has been handed over to him by the
FDP. The man at the right has communications lines that connect him
with the radio truck associated with the SCR-584 station, with a radio
direction-finding station, and with the FDP under which the SCR-584 is
operating.

The 180° plotting table used with the SCR-584 was admittedly a

Fig. 716.—-Interior of SCR-584 modified for close control, showing 180° plotting board.
Near Cologne, December 1944.

makeshift, and there was later designed a plotting board, shown in Fig.
7-17, which embodied many improvements. It plots in rectangular
rather than in polar coordinates, contains “smoothing” circuits that
greatly improve the accuracy of the plotted aircraft position, and draw's
an ink record of the position of the aircraft being tracked, so that the
controller has a knowledge of the aircraft course, as well as position, at
all times. This device also plots in ground range rather than in slant
range.

The range at which aircraft can be tracked by the SCR-584 can be
greatly increased, and the accuracy of tracking somewhat improved, if an
airborne beacon (Chap. 8) is carried in the aircraft under control. Such a

240

THE EMPLOYMENT OF RADAR DATA

[Sec. 7-8

beacon also facilitates identification of the plane to be controlled at the
time of initial pickup.

The operational use made of the SCR-584 as modified for aircraft
control was basically any that required precise navigation under restricted
visibility. Large aircraft could carry radio and radar navigational aids
which often made it possible for them to carry out such missions without
assistance, but the fighters and fighter-bombers of the TAC’s had neither

Fig. 7-17.—X-Y plotting board for SCR-584.

space nor operators for such equipment. Their navigational aids had
to be external to the aircraft.

A total complement of 8 officers and 38 enlisted men was required to
operate a single control SCR-584, the majority of these men belonging to
the organization involved in making use of the radar data.

7-8. Teleran. —The examples of operational radar systems will be
closed with a brief account of a system still in the developmental stage.
It is called “Teleran” (for Television Radar Air .Navigation) and
involves the coordinated use of air and ground equipment.

The basic idea of Teleran is that high-performance ground radar, if
supplemented by simple and reliable height-finding means and by

Sec. 7 - 8 ]

TELERAN

241

weather and route information, can provide all of the data needed by
aircraft for en-route navigation and for airport approach. Further, high-
precision ground radar can supply all the information that a pilot requires,
in addition to his own flight instruments, for instrument approach and
landing. All that is required is to get this information into the aircraft,
where it can be displayed to and used by the pilot.

It is proposed to add to the display of a ground radar a chart that
contains map, airways, and weather information of interest to pilots, and
to send the resulting picture by television to the aircraft, where it is dis¬
played to the pilot. Televising of the display is preferred to the use of
the radar-relay methods described in Chap. 17 because television does
not require the use of persistent phosphors, with their low maximum
level of light intensity, in the aircraft cockpit, where the level of ambient
light is likely to be high.

On the basis of the assumption that display of all aircraft in the pic¬
ture offered a pilot would be useless and confusing, it is proposed to
separate the radar signals according to the altitude at which the corre¬
sponding aircraft are flying. Thus, for example, a pilot at 5000 ft would
be sent signals showing the positions of all aircraft in his neighborhood
and in the altitude range from 3500 to 6000 ft. This can be accomplished
technically by supplying each plane with a transponder beacon whose
reply signal is coded (Sec. 8.8) in accordance with the altitude at which
the plane is flying. This coding can be controlled automatically by an
altimeter. At the ground radar station, signals in the various altitude
intervals can be sorted out and displayed separately for transmission to
aircraft using the system. The transponder also increases the range of
the radar equipment and, if a reply frequency different from the trans¬
mitter frequency of the radar is used, eliminates difficulty from ground
echoes which might interfere with seeing low-flying aircraft.

Figure 7T8 shows a Teleran display as it might appear to a pilot
flying at 11,000 ft. At this altitude, since topographical features are of
little interest, nothing is shown except other aircraft, towns, airports,
airways, frequency channels in use by Teleran ground stations, and the
direction and velocity of the wind. To assist the pilot in flying a course,
the compass reading is repeated on a disk mounted over the face of the
indicator and ruled with parallel lines showing the heading of the aircraft.
These lines are shown dashed in Fig. 7T8.

It is essential for the pilot to know which of the beacon responses is
that of his own plane. This is accomplished by having a rotating radial
line, centered at the radar station (which appears in the center of the
picture), form part of the display information transmitted from the
ground station. This line is normally invisible, but the television receiver
is controlled by a signal from the transponder in such a way that the line

242

THE EMPLOYMENT OF RADAR DATA

[Sec. 7-8

appears bright when the beacon is being interrogated. Since the beacon
is interrogated only when the radar is pointing at it, the bright line passes
through the signal pip representing the individual plane carrying the
equipment. Each pilot sees a different radial line indicating his own
plane.

Fig. 7 18.—Schematic drawing of Teleran presentation in an aircraft flying at 11,000 ft.

The Teleran system has been worked out in much more detail than
can be described here. Enough has been said to indicate the fashion in
which system planning, based always on the needs of the user, leads to a
functionally simple but technically elaborate final result, embodying not
only radar but also beacons, television, aircraft instruments, and always—
inescapably—men.

CHAPTER 8

RADAR BEACONS

By L. A. Turner

Introduction .—Radar waves are reflected by targets of different sizes
regardless of their importance to the user of a radar set. The echo from
an aircraft may be lost in much larger echoes from near-by mountains, or
it may become too weak to be followed to ranges as great as desired. The
echo from a friendly aircraft is like that from a hostile one. The exact
location of a place on the ground may be of importance to a radar-
equipped aircraft even though there is no distinguishable radar target
at that point. In nearly all cases where it would be advantageous if an
echo could be made much stronger or more readily distinguishable from
other confusing ones, the use of a radar beacon is indicated. (An enemy
aircraft obviously constitutes one difficult exception.)

The usefulness of beacons was demonstrated with the early radar sets
that were operated at long wavelengths. A large proportion of the
beacons used in the war operated at frequencies about 200 Mc/sec.
These included the beacons used with ASV Mark II search radar, the
transponders used for identification, the portable Eureka beacons that
were part of the independent Rebecca-Eureka beacon system, and a
much-used system for precise bombing, the Oboe Mark I. Another
system for precise bombing, the Gee-H system, used beacons of even
lower frequency. In this chapter, more emphasis is put on the newer bea¬
cons at higher frequencies since the trend in radar is toward microwaves.

The beacon is essentially a repeater of radar pulses. It has an
antenna and receiver that convert pulses of energy, received at high
frequency from a radar set or special interrogator, into triggering signals.
Each such signal triggers the transmitter in the beacon and causes it to
radiate one or more pulses of radio energy that may have almost any
desired power, frequency, duration, number, and characteristic spacing.
Figure 8T gives a block diagram of a beacon. Since it takes time for the
beacon to react, the first reply pulse comes back to the radar set slightly
delayed and indicates a range slightly greater than the true one. In
many applications this delay is negligible, in others it is made to have a
constant known value for which allowance can be made. The delay can
be kept down to a few tenths of a microsecond when necessary. In the
special case where the radiated pulse is single, has approximately the

243

244

RADAR BEACONS

[Sec. 8

duration and frequency of the radar pulse, and is not appreciably delayed,
the beacon acts somewhat like an echo amplifier. The intensities of
received and transmitted signals are, to be sure, independent, rather than
in fixed proportion as in the case of a true amplifier. In general, however,
the frequency of the reply will be different from that of the triggering
radar set. In order to receive such replies, one needs a receiver tuned to
the frequency of the pulses sent out by the beacon instead of to the fre¬
quency of the initial transmitted pulses. This may be either the receiver
of the radar set tuned to the new frequency, or a second independent
receiver tuned to the beacon. In either case, the receiver of the beacon
signals does not receive radar echoes since it is not tuned for them. Thus,

Receiving
antenna

Fig. 8-1.—Block diagram of a beacon.

the beacon signals are separated from radar reflections and can be dis¬
played without being swamped by heavy permanent echoes. Also, since
the pulse power of the beacon transmitter can be made as great as
desired, there is no limit to the strength of the reply. The range is
limited only by the power of the radar transmitter and the sensitivity of
the beacon receiver, which determine whether the beacon transmitter is
triggered or not. Figure 8-2a shows the radar echoes and Fig. 8-26 the
beacon replies on the indicator of the same 3-cm radar set. The pictures
were taken one immediately after the other on the same flight.

By its very nature, the radar-beacon combination involves two send-
receive links as does any two-way communication system. The two
links are ordinarily connected automatically in a simple regular way and
are uninfluenced by human reactions. Since the channels exist, how¬
ever, they afford the basis for a communications system. In the past,

Sec. 8]

RADAR BEACONS

245

Fia. 8-2.—Radar and beacon signals of a 3-cm radar set: (a) shows only the radar echoes,
(b) shows the beacon reply; both were received at nearly the same position.

246

RADAR BEACONS

[Sec. 8-1

beacons have sometimes been used in providing communication systems
of a rudimentary sort and also for exercising remote control. Intelligence
has been conveyed from the radar to a beacon-carrying vehicle by modi¬
fication of the repetition rate, the length of interrogating pulses, their
spacing in groups, or the duration of the intervals of interrogation. The
replies of the beacons have also been modulated in such ways. One
200-Mc/sec beacon was used for two-way voice communication while still
functioning for its normal use. For the most part, however, this use for
communications has been somewhat incidental. Much fuller use of the
channels could be made since the portion of the spectrum required for
transmission of beacon signals of a simple sort is ample for conveying
much more complicated intelligence.

Beacons of the synchronous sort just described have been variously
called “radar beacons,” “responder beacons,” “racons,” and “trans¬
ponders,” there being no essential distinctions among these terms. The
discussion here is confined to such beacons since other free-running types,
more like ordinary radio beacons, appear to be less useful in conjunction
with radar sets. From the free-running type, only the bearing can be
determined. Radar information is particularly useful because it gives
accurate determinations of range; it is obviously sensible to provide, as
an adjunct to radar, the sort of beacon that makes the best use of this
property.

This chapter aims to give a brief resume of the main points involved
in the use of radar beacons. The design of beacons and of systems using
them is treated at length in Vol. 3 of this series.

RADAR-BEACON SYSTEMS

8T. Types of Radar-beacon Systems. —In a discussion of beacons
it is convenient to classify them as fixed ground beacons, shipborne
beacons, airborne beacons, and portable beacons. All of these may be
used in conjunction with ground, ship, or airborne radar sets, or with spe¬
cial interrogator-responsors. The following combinations have proved
useful so far:

Ground Radar.

Shipborne beacons. This combination is of use principally for
identification of particular ships since, in general, the radar echo
from a ship is distinct enough.

2. Airborne beacons. This combination has proved to be of great
usefulness for identification and for various purposes where ground
surveillance and control of air traffic is desired. Figure 8-3 shows
the AN/APN-19, an airborne 10-cm beacon.

A special system of precision bombing, known as the “Oboe

Fig. 8-3.-—Component parts of the AN/APN-19 beacon. The AN/APN-19 is a 10-cm
beacon designed for installation in aircraft.

The position of ground radar sets can sometimes conveniently be
fixed by measurement of ranges to portable beacons placed at
known points.

Ship Radar.

1. Fixed ground beacons. The beacon is here the radar analogue
of the old-fashioned lighthouse. Since range to the beacon is
measured as well as its bearing, observation of a single beacon gives
two intersecting lines of position and a fix more accurate than is
customarily obtained by other methods.

2. Shipborne beacons. This combination can be of use principally
for identification.

3. Airborne beacons. Beacons have facilitated control of military
aircraft from a ship, and have been useful for identification of air¬
craft. In the past war, they were used to enable ships to home on
aircraft that were orbiting in regions where submarines had been
sighted.

Special systems designed for measuring with great accuracy the
ranges from two ground beacons at known positions have been
used for mapping and blind bombing of high precision. Since in
such systems there is no need for determining azimuth, lower fre¬
quencies can be employed advantageously, omnidirectional
antennas can be used in the aircraft, and the beacon replies (which
are then steady) can be presented on special indicators designed
for ease in getting great accuracy of measurement.

Beacons at longer wavelengths have been used in blind-
approach systems.

2. Shipborne beacons. Some beacons have been used for identifying
ships, others for enabling aircraft to home on their carriers or on
convoys.

Fig. 8-4.—The AN/CPN-6 beacon. The AN/CPN-6 is a high-powered 3-cm beacon
intended for use in permanent installations on the ground.

4. Portable beacons. Small beacons have been used for marking life
rafts and small target rafts.

Airborne Radar.

1. Fixed ground beacons. Beacons used with microwave radar hav¬
ing PPI presentation give most satisfactory navigational fixes by
graphically locating the aircraft with respect to several known
points on the ground. Figure 8-4 shows one of the AN/CPN-6
beacons, a 3-cm beacon of high power designed for use in air
navigation.

248

RADAR BEACONS

[Sec. 81

Sec. 8TJ

TYPES OF RADAR-BEACON SYSTEMS

249

3. Airborne beacons. This combination has been useful as an aid in
effecting rendezvous and for identification.

4. Portable beacons. Such a combination has been of military use
under circumstances where fixed ground beacons could not be set
up readily, but small portable beacons could be used instead.

r. i

{ ]

Fig. 8-5—The AN/PPN-2 beacon. Fig. 8-6.—The AN/UPN-1, a portable
The AN/PPN-2 is a 1.5-m beacon de- battery-operated 10-cm beacon,

signed for use principally by paratroops.

Such beacons have been used principally to indicate to supporting
aircraft the location of isolated forward elements on the ground,
such as advance parties of paratroops or secret agents. Figure
8 5 shows the AN/PPN-2, a 1.5-m beacon carried by pathfinder
paratroopers; Fig. 8-6 shows the AN/UPN-1, a 10-cm beacon that
was similarly used. Similar beacons have been used for marking
life rafts at sea.

250

RADAR BEACONS

[Sec. 8-2

Table 8-1 collects and summarizes all these applications.

Table 8T.—Summary of Principal Uses of Beacons

Radar or
other

interrogator

Beacons

Ground

(fixed)

Shipborne

Airborne

Portable

Ground

Identification

Identification
Ground-controlled
precise navigation

Surveying

Shipborne

Pilotage 1

Identification

Control of aircraft
Homing

Life rafts

Shore bombardment

Airborne

Navigation
Blind ap¬
proach

Identification

Homing

Identification

Rendezvous

Temporary marking
of points on land
Life rafts

8-2. Systems Planning. —Given a particular radar set, it is simple
enough to provide a beacon for any special use. The receiver of such a
beacon can be of narrow bandwidth and tuned to the frequency of the
radar. The reply can be either at the same frequency or at one just
different enough to permit separation of radar echoes and beacon replies,
but still receivable merely by minor adjustment of the radar receiver.
When, however, it is desired to provide a beacon that will be useful to
many different radar sets of the same type, the problem is more compli¬
cated. Radar sets of a given kind are usually operated at somewhat
different frequencies in order to avoid mutual interference. Thus, the
receiver of the beacon has to have sufficient bandwidth to receive the
interrogating signal from any one of the radar sets. For airborne 3-cm
radar sets, for example, the band from 9320 to 9430 Mc/sec was used.
This band of 110 Mc/sec was needed to take care of the variations of the
frequencies of the magnetrons as manufactured plus further changes to be
expected in adjustment and use in the field. The reply, however, had
to be made at some particular frequency; that used was 9310 + 2 Mc/sec.
Provision must be made in the radar receiver for quick and accurate
tuning to a chosen beacon reply frequency if beacon signals are to be used.

Radar sets and beacons cannot be so designed without careful plan¬
ning. If the full potentialities of radar beacons are to be realized, both
radar sets and beacons must be planned together as parts of a unified radar-
beacon system. This now seems trivially obvious, but it is not the way
that much of the existing equipment was designed. In the development
of radar, the beacons came as an afterthought. The result was that

Sec. 8-3J

GENERAL IDENTIFICATION SYSTEMS, IFF

251

beacon performance often was not so good as can be obtained. The
designer of future radar systems, having knowledge of radar and radar-
beacon possibilities, should decide on the scope of desired operational
characteristics of his system and then design his radar set and beacons
together in order to achieve the result most efficiently.

If the frequency of the beacon reply is to be very different from the
frequency of the radar transmitter, it is usually necessary to provide a
separate antenna and receiver for the beacon signals. The scanning of
this second antenna must then be synchronized with that of the radar
antenna. In some cases, this synchronization has been accomplished
by using the same parabolic reflector with separate feeds for the two
frequencies.

If the frequency cf the beacon is close to that of the radar set, other
problems arise. The same antenna can be used, but then the design of
the duplexing system becomes more complex than it is for the simple
radar set. Attenuation of the received signals at both frequencies must
be held to a small amount.

In any case, it is desirable to include some device that will automati¬
cally keep the local oscillator for beacon signals in tune. When the
beacon receiver is completely separate from the radar receiver, it is
advantageous to provide switching arrangements so that the radar
operator can have his choice of either radar or beacon signals alone, or
both together. It is often useful to include separate adjustments for the
saturation levels of the signals, so that stronger beacon signals will stand
out when superimposed on saturated ground “clutter” from the radar.
Also, if the pulses of the beacon are short, it is possible to improve the
display by stretching them in the video amplifier of the receiver.

Some beacons are made to reply only to interrogating pulses of proper
length, or to those having other special characteristics, as discussed
below. In such cases, the corresponding changes have to be included
in the modulator of the radar set, with appropriate controlling switches.

The above list of radar design features needed for best use of beacons
appears somewhat formidable, and so it is when one is trying to patch
up an antique radar set that does not have such features included in its
original design. When starting afresh, however, the fist does not involve
unreasonable additional complications. Actually, the most compact
airborne microwave radar set produced during the war was also by far
the most simple to operate, and it incorporated nearly all of the features
mentioned above. This set, designated AN/APS-10, is described in
Chap. 15 of this book.

8-3. General Identification Systems, IFF. —The discussion of this
chapter is confined almost entirely to the use of beacons for various
navigational problems and for identification systems of somewhat

252

RADAR BEACONS

[Sec. 8-4

restricted scope. Mention should be made, however, of the more general
problem of identification, which gave rise to a system known as IFF—
Identification of Friend or Foe. This system was probably the most
important single field of application of radar beacons in the war. The
goal was to provide every friendly military ship and aircraft with a trans¬
ponder that would give an identifying reply signal in response to proper
interrogation. Since the location of the ship or aircraft in question was
almost always determined by radar, the problem was actually one of
determining the friendly or hostile character of radar targets. The IFF
interrogating equipment was thus used in the great majority of cases as
an adjunct to a radar set. The problem was enormously difficult in view
of the rapid development of many types of radar sets in both Britain and
America,, the tremendous density of airplane traffic to be dealt with in
many theaters and the necessity for having replies coded with sufficient
elaborateness to prevent the effective use of captured IFF transponders
by the enemy for deception. In addition to these and other inherent
technical difficulties, there were still others of a political sort. Among
these were the problems of getting agreement among the many branches
of the British and U.S. Armed Services concerning details of desired
characteristics of systems and of planning manufacture, distribution,
installation, and maintenance of equipment in such a way that an IFF
system could actually go into effective widespread use in a theater by
some target date. It seems that problems of this sort are to be encoun¬
tered in connection with any such system that is meant to have wide¬
spread use. In spite of all these difficulties, one such system was put
into use in nearly all theaters, and was of great help where its potentiali¬
ties were understood and its limited traffic-handling capacity was not
exceeded. It is beyond the scope of this chapter to go further into the
problems of IFF. A peace-time requirement that is likely to pose prob¬
lems of similar character, although of lesser complexity, is that of control
of air traffic in the neighborhood of airports where the traffic is likely to
be heavy.

8-4. Radar Interrogation vs. Special Interrogators. —Much of the
preceding discussion implies that beacons are to be used principally with
radar sets and to be interrogated by them. For IFF, however, because
of the great variety of radar sets at different wavelengths, it is necessary
to pick particular bands of frequencies for the IFF beacons and to supply
supplementary interrogating equipment to work with the radars. For
every proposed radar application where beacons would be of use, the
question will arise whether it is better to use radar beacons or to provide
such separate equipment to work at frequencies set aside for the purpose.
There seems to be no single correct answer. Separate cases must be
considered separately, but it is desirable that in so doing the proposed

Sec. 8.4] RADAR INTERROGATION F£. SPECIAL INTERROGATORS 253

systems be conceived as broadly as the possibilities for unified planning,
control, and operation will permit.

Let us first consider the planning of beacons for use with airborne
radar, which has been the subject of some controversy in the past. If
radar beacons are to be provided, a whole new set of them is required for
every new band of frequencies used. British opinion has inclined to the
view that the resulting multiplicity of beacons is intolerable, that it
involves far too great a cost for the design, manufacture, installation, and
maintenance of these many different beacons. The British policy has
been to design for every radar set a supplementary synchronous beacon
interrogator for interrogating beacons in the 200-Mc/sec region and
receiving replies at such a frequency, the replies to be displayed whenever
possible on the indicator of the radar set. These interrogators were
to be replaced in due course with similar equipment operating at a new
and higher region of frequency. Special separate antennas are obviously
required. The contrary view, more widely held in the United States, is
that the provision of suitable beacons is but a small part of the over-all
complication and expense of introducing radar in a new band of fre¬
quency; that the frequencies used for radar sets for any given purpose
tend to group in a small number of reasonably narrow bands; that
since the radar set itself can be as good an interrogator-responsor as
one could desire, it is putting complication in the wrong place to add more
equipment to a crowded airplane; and that the display of the beacon
signals and the performance as a whole will be inferior when the beacon
frequency is considerably below the radar frequency.

The decision must depend, to a considerable extent, on the relative
importance of using beacons for navigation and for identification. For
an identification system, it is obviously necessary to have but one rela¬
tively simple type of beacon and to require that the identifying radar sets
be accommodated to it. For navigational purposes, the requirements
of the airplane become relatively more important.

If all information needed for the desired use can be obtained with
beacon signals alone, it is not necessary to have a proper radar set at all,
and the radar set can then be replaced by an interrogator-responsor.
This has a transmitter and receiver like those of a radar set, but it is in
general somewhat smaller and lighter since not so much transmitted
power is required for triggering beacons as is required for getting adequate
radar echoes. Such equipments can be especially economical in size and
weight if range only is wanted, or if the sort of azimuth information
obtainable by lobe-switching is adequate. In such cases the sets can be
run at low frequencies, and the equipment is relatively compact. If,
however, it is desired to have PPI presentation of the beacon signals,
which affords azimuth information comparable to that given by modern

RADAR BEACONS

254

[Sec. 8-5

radar sets, the interrogator-responsor becomes so nearly a complete radar
set that it may as well be made to be one.

In the case of beacons carried by aircraft to extend the range and to
facilitate identification by ground radar sets, it is obviously desirable to
have only one type of beacon for all aircraft under the surveillance of a
comprehensive system of like ground radar sets. It is also desirable that
these beacons give signals of the same degree of resolution in azimuth as
that of the radar signals. It seems likely that the radar sets and beacons
will be designed together as parts of a system operating at 3000 Mc/sec
or higher. There appears to be little to be gained by trying to have this
system operate at the same frequencies as the beacons for use with air¬
borne radar sets unless it is required that the same beacons that are to be
interrogated by the ground radar sets also reply to interrogation by
airborne radar sets.

8-5. Independence of Interrogation and Reply. —Although the funda¬
mental considerations that underlie the design of beacons and beacon
systems are the same as those for radar in general, there are certain con¬
sequences of the almost complete independence of the interrogation and
reply links that need explicit mention.

Range. —The expression for the power received by the beacon is given
by Eq. (2T4). For its maximum value, using a notation defined below,
we get

(Psi)

PTi(GTi)mti (Gs> )mii ‘ Xf

16tt 2 R 2

(1J

Subscript i-interrogation leg.

Subscript r-response leg.

Subscript ^-transmitting components.

Subscript ^-receiving components.

R = distance from interrogator to beacon
X = wavelength of the radiation
P = power in watts.

G a = maximum value of effective gain.

(/*«)— = maximum value of the available peak power received by
the beacon.

P T i = peak value of the power transmitted by the interrogator
(radar).

(Gr.)m.x = maximum value of the gain of the transmitting antenna
of the interrogator.

{G S i) m.i = maximum value of the gain of the receiving antenna of the
beacon.

X; = transmitted wavelength.

If we let P° si represent the peak value of available received power
necessary for triggering the beacon and /?“ represent the corresponding

Jsame units.

Sec. 8-5] INDEPENDENCE OF INTERROGATION AND REPLY 255
range, Eq. (1) gives

P Ti

(/-* Ti) * Si) u

( 2 )

In Eq. (2) R “ is the maximum free-space range for interrogation of the
beacon; when it is at greater ranges it will not be triggered.

The corresponding expression for the reply link is

R° r =

4ir

P Tr

((?!>) rum (6\S

(3)

In Eq. (3), P° s , is the peak value of the available received power
required to give a satisfactory beacon signal on the indicator of the
interrogating system, due account being taken of scanning losses and
other circumstances of use. The range R° r is the greatest one for which
reply signals from triggered beacons will be usable. This cannot be
defined as clearly as is R] since having a signal “satisfactory” is less
definite than having it either present or absent. The other quantities
in Eq. (3) are of obvious significance if it is kept in mind that the sub¬
script r refers to the reply link.

In the preceding paragraphs it was assumed that the triggering of the
beacon and the intensity of the displayed reply depend on the pulse
powers of the two pulses. This implies that both the receiver in the
beacon and the one in the interrogating system have a bandwidth suffi¬
cient to insure that both received signals rise to a value that depends on
the pulse power and is independent of the length of the pulse within wide
limits. This condition is usually the desired one and the receivers are
designed accordingly. If a receiver of very narrow bandwidth should
be used, however, the peak value of its output would then depend upon
the energy of the pulse, rather than upon the pulse power. For such
cases Eqs. (2) and (3) would be modified by substituting the transmitted
and received values of the energies per pulse for the respective pulse-
power values.

It is sensible to design the system so that R° r ~ since there is no
use in having replies that are too weak to be observed even though the
beacon is being interrogated, as can be the case if R° r < R\. Likewise
nothing is gained by making provision for strong replies if they are absent
because of the failure of the interrogation. This situation can arise if
m > R% The common value of R’l = R° r must be made equal to the
desired maximum range, and indeed somewhat larger if a reasonable
factor of safety is desired. It is sometimes useful to make R° r somewhat
larger than R° in order to facilitate recognition by the operator of beacon
signals in the noise.

256

RADAR BEACONS

[Sec. 8-5

In the case of beacons interrogated and received by a radar set, X r is
nearly equal to X,; (GT>)«... usually equals (G Rr ) m „ since the same antenna
is likely to be involved; and (G Ri ) m „ usually equals (G Tr ) m „ since beacon
antennas for receiving and transmitting need to have the same radiation
pattern and are therefore alike. The condition for balance of the two
links, namely that R1 equal R°, then becomes

P Ti /P° si = Ptt/P° St or P Tr /P T , = P°JP° si - (4)

The receiver of the beacon is almost always less sensitive than that of the
radar, either by necessity (because of the greater bandwidth), or by
choice to avoid undesired triggering (see below); hence P° Sr < P° si . In
the balanced system, then, the transmitter of the beacon may as well be
less powerful than that of the radar in the same proportion.

In actual cases, Eq. (1) and a corresponding equation for the received
power in the reply link involve two additional factors. One of these is a
geometrical factor that expresses the effects of interference and diffrac¬
tion. The other takes account of the attenuation of the radiation in the
atmosphere. These matters as they pertain to radar echoes are dis¬
cussed in Secs. 2T2 and 2T5. It should be noted, however, that the
numerical factors appropriate here are the square roots of those for radar
signals, when for the latter the effects on both the transmitted and
reflected pulses are lumped together. These factors drop out of the
expression (4) just as the antenna gains do, since they have the same value
for both links. In any beacon system in which the frequencies of inter¬
rogation and reply are substantially different, however, all of the factors
in Eqs. (2) and (3) must be retained and these additional ones must be
added. The two links have to be designed separately to get proper
operation at all ranges up to some fixed value or to meet other particular
requirements.

It is apparent from Eq. (1) that another consequence of the inde¬
pendence of the two links is a different law for the relation between signal
strength and range. Radar echoes vary in pulse power as the inverse
fourth power of the free-space range, whereas beacon replies vary only as
the inverse square. In general, beacon signals do not vary as much
between particular values of range, do not cut off as abruptly with
increasing range, and do not give as deep interference minima as radar
signals do.

Azimuth .—One further consequence of the separation of the two links
is that the scanning sector through which beacon replies are obtained is
limited either in the interrogation link or in the reply link according to
circumstances. Equation (1) becomes more generally

n PT 0TiG liN\

( 5 )

Sec. 8-5] INDEPENDENCE OF INTERROGATION AND REPLY 257

Here Pr, is the available pulse power at the beacon for any relative posi¬
tion of the interrogator and the beacon. The gain of the transmitting
antenna, G T i, is a variable that depends upon the angular position of the
antenna with respect to the line from it to the beacon. The received
power is a maximum only when the interrogator is really looking at the
beacon. Similarly G Ri , the gain of the beacon receiving antenna, is a
variable depending on the orientation of the antenna with respect to the
line from the beacon to the interrogator.

Let us consider, as an example, a ground radar set scanning around
through the complete azimuth circle and interrogating an airborne bea¬
con. Curve a of Fig. 8-7 represents schematically a polar diagram of the
logarithm of the power received at
the beacon as a function of the angu¬
lar position of the radar antenna.

The line to the beacon is assumed
to be the upward vertical. In the
ideal case the curve is the same as
the antenna pattern of the radar; in
actual cases it is often modified by
reflections from near-by buildings,
hills, etc. If circle b represents the
threshold power for triggering, the
beacon will be triggered only through
the sector AOA'. If, however, the
values of received power should all
be increased by 12 db or so (by de¬
creasing the range to the beacon),
the beacon would also be interrogated
by side lobes of the antenna. Figure
8-8 shows this effect. It is clear that
if we consider interrogation that
begins when the separation is first
large and then decreases, the beacon
is first interrogated at maximum range through a very narrow angular
region. As the range decreases, the sector of interrogation increases, but
remains of the order of magnitude of the half-power beam width of the
antenna until a range about one tenth of maximum is reached. There,
assuming the side lobes of the antenna pattern to be about 20 db
down, side-lobe interrogation begins and grows wdth decreasing range.
Finally, in practical cases, a range is reached for which the beacon is
interrogated no matter which way the antenna is pointed. It is also clear
that reduction of the radiated power would produce a narrowing of the
sector of interrogation of any particular beacon, but would lead to failure
to interrogate those at greatest range.

Fig. 8-7. —Schematic logarithmic polar
diagram of the antenna pattern of a
microwave radar. The triggering of a
beacon occurs when the energy radiated
in a given direction is in excess of some
necessary minimum amount.

258

RADAR BEACONS

(Sbc. 8 5

Similar considerations apply to the reply link. If we assume the
beacon to be interrogated for all angular positions of the antenna of the
interrogator and the sensitivity of the receiver to be kept constant,
the angular width of the beacon arc on the PPI tube will vary as did the
sector of interrogation in the previous case. Over a large distance the
reply arc will be of the order of magnitude of the half-power beam width of
the receiving antenna. For close-in beacons, extensions attributable to
side lobes appear, and for very close beacons a complete circle is obtained.
The complete circle or side-lobe pattern can be reduced to the narrow arc
by suitable reduction of the gain of the radar receiver, again with the
loss of more distant beacons. Here, however, it is possible to use a

Fig. 8-8. — Interrogation of a beacon by side lobes. Interrogation of a shipborne
10-cm beacon by a radar set on Mt. Cadillac on Mfc. Desert Island, Me. (a) shows the
extended pattern at about 4 o’clock in the picture; ( b ) shows how it can be reduced to the
reply in the main beam by manipulation of the gain control of the receiver of the beacon
signals.

sensitivity-time-control (STC) circuit that gives automatic variation of
the sensitivity of the receiver as a function of the elapsed time after emis¬
sion of the interrogation pulse. The gain is thus automatically adjusted
to be correct for beacons at all ranges with the result that they all appear
as approximate half-power beamwidth arcs. This circuit must be care¬
fully designed if it is to give good results with ground radars interrogating
beacons on aircraft flying in the maximum of the pattern of the receiving
antenna and still not unduly attenuate weaker replies from beacons in
low-flying aircraft.

It is clear from the foregoing that the width of the reply arc is always
limited in either one link or the other, whichever is the narrower, and that
it can be controlled by adjusting either transmitted power or receiver
gain. Where manual adjustment for good reception of a particular
beacon is to be used, cutting down the transmitted power would be

Sec. 8-5] INDEPENDENCE OF INTERROGATION AND REPLY

259

preferable since overinterrogation is thereby minimized. Manual adj ust-
ment would be helpful in systems where a large number of airborne radar
sets are likely to be interrogating some particular beacon on the ground
or on a ship. This procedure has not been used so far, however, since
the reduction of the transmitted power usually requires more complica-

Fio. 8-9.—Replies from an experimental beacon interrogated at 10 cm and replying at
1.5 m. The exposure was continuous; the strong radial line in the picture is therefore made
up of the successive beacon replies. The sweep was delayed, so that the replies extend
from 50 to 100 miles.

tion of the radar set than does reduction of the receiver gain. Automatic
adjustment of the sensitivity of the receiver is more appropriate for
ground radar sets interrogating airborne beacons at many different
ranges, or wherever the operational simplicity of automatic adjustment of
gain is more important than the avoidance of possible overinterrogation.

It has proved convenient for some purposes to provide beacons which
are interrogated by microwave radar sets and which reply at a frequency

260

RADAR BEACONS

[Sec. 8-6

lower than that of the radar by a factor of 20 or so. Either the beam-
width of the antenna for receiving replies from the beacon is made very
broad or this antenna is made omnidirectional. Microwave angular
discrimination is still provided by the sharpness of the interrogating
beam—again only for beacons at ranges beyond that for which side lobes
begin to cause broadening of the reply. Figure 8-9 shows a whole set of
replies from such a beacon, exposures having been made every few sweeps
of the PPI. The interrogations were at 10 cm, the replies at 1.5 m. The
principal reason for using such a beacon rather than one that gives a
microwave reply is the relative simplicity of the low-frequency trans¬
mitter and antenna of the beacon. Also, by placing several simple
antennas and receivers for the interrogation at different places on an air¬
craft, it is possible to achieve a good approximation to an effectively
omnidirectional pattern for the interrogation link. This is almost
impossible to achieve with single simple microwave antennas because of
interference effects. It is necessary to put the outputs of such multiple
receivers in parallel after detection so that there will not be a combination
of r-f signals in varying phases to give rise to interference maxima and
minima.

The foregoing discussion implies that the broadening of the arcs for
beacon replies is greater than that for radar signals. This is not the case,
however, if the maximum range for both is the same. If and G(, ob€)
are the respective gains of the antenna at the center of the pattern and at
the maximum of the first side lobe and and Ri ( u>be) the corresponding
maximum ranges for interrogation of the beacon (to give minimum
triggering power), from Eq. (5) we get = G(lob«) / RiQobe) ■

The same line of argument followed through with the radar equation
gives GL,/(if“) 4 = G 2 (i„b.)/E 4 ,i ob .„ which gives the same value of
when R1 is the same. In practice, however, the broadening of the beacon
signals is likely to be greater since it is customary and usually desirable
to set the sensitivity of the beacon receiver so that the maximum free-
space range is considerably greater than the radar range to an average
target. This is done partly to ensure increased range and partly to allow
for the considerable unavoidable variations between the receivers of
different beacons as installed and operated.

8-6. Frequency Considerations. General .—Since beacon replies are
much like radar echoes, the considerations involved in choosing the fre¬
quency region for a system in order to get the desired resolution are much
the same. In general, the higher the frequency, the better the azimuth
discrimination for a given tolerable size of antenna system. This
advantage of improved angular separation with increased frequency is
somewhat offset by a tendency toward increased size and weight of trans¬
mitters needed for a given range performance.

Sec. 8 6] FREQUENCY CONSIDERATIONS 261

The most satisfactory presentation of beacon replies for purposes of
ordinary navigation is undoubtedly the PPI since it gives the whole
situation at a glance in a direct way. The angular widths of beacon
replies should be limited to a few degrees, if possible. For an airborne
interrogator this suggests the use of 3-cm or shorter wavelength; for
systems having ground interrogators with large antenna arrays a con¬
siderably lower frequency can be used. Azimuth determination by lobe¬
switching, involving comparison between the strengths of signals received
on two antennas pointed in different directions, is adequate for many
purposes but relatively clumsy in use. It permits the use of lower frequen¬
cies and much broader antenna patterns, with corresponding reduction
in size of the antennas, but it results in a great increase in the diffi¬
culty of identifying beacon replies with particular radar echoes. It is,
however, satisfactory for aircraft homing on the beacon. In the wartime
systems which provided means of precise navigation by accurate measure¬
ment cf the ranges to two ground beacons at known positions, special
indicators were used. They displayed and measured the positions of the
steady beacon signals obtained by using omnidirectional antennas rather
than scanners.

There is an upper limit on the frequency to which it is desirable to go.
At about 15,000 to 20,000 Mc/sec the attenuation by water vapor in the
atmosphere of the earth begins to become of consequence. In conditions
of bad weather, when navigational beacons are most needed, the range of
beacons at such frequencies would be lowered so much that they would
be of little use.

In nearly all cases, the frequency of the beacon reply should be differ¬
ent enough from that of the interrogating pulses to obviate simultaneous
reception of beacon replies and radar echoes by one receiver. In this way
the swamping of beacon replies by strong echoes is eliminated. Even
when it is desirable that radar echoes and beacon replies be presented
simultaneously, the saturation video levels for the two kinds of signals
can be made different by using separate receivers; thus beacon replies can
be made to stand out even when superimposed on saturated ground clutter.
A very striking differentiation between radar and beacon signals from
aircraft has been achieved by putting them on separate PPI tubes that
give signals in two different colors, the signals being effectively super¬
imposed by optical means.

If any interrogator or radar set of a given type is to be able to locate a
beacon readily, the beacon must transmit at some known frequency and
the receiver for the signals must be readily tunable to that precise fre¬
quency, whether the beacon replies are received or not. When the loca¬
tion of the beacon is unknown (as is usually the case) and the interrogator
is scanning, it is not tolerable to increase the general uncertainty about

262

RADAR BEACONS

[Sec. 8-6

the beacon by having to search over a band of frequencies. Thus, ade¬
quate stabilization of the beacon transmitter is required, and the receiver
for the signals must have automatic frequency control, or a wavemeter
must be provided, or it must be possible to set the frequency accurately
to preset values by having mechanical parts of sufficient precision. All
of these techniques have been worked out and are now available.

This use of a spot frequency for the reply does have a disadvantage,
however. Each interrogating radar will receive not only the responses
of the beacon to its interrogation pulses, but also the beacon responses to
interrogating pulses from other sets. The replies that a radar set receives
to its own pulses are synchronous and appear at the proper range in a
regular way. Replies to other radar sets are, in general, not synchronous.
This is discussed further in Sec. 8-9.

Fig. 8-10.—Variation of frequency with time in a beacon. With sweeps as in (a), equal
intervals between replies will be obtained for all frequencies. For (b) the distribution
depends on the frequency.

Sweeping Frequency .—In some cases it has not been feasible to use a
single spot frequency of reply either because the number of replies at the
frequency would be excessive or because it was not practical to modify a
group of radar sets to receive the chosen frequency. In these cases,
beacons have been used in which the common frequency of receiver and
transmitter was made to sweep periodically over the band of frequencies
of the interrogators. A given interrogator got replies when the beacon
came into tune with it. This system is useful only with interrogators
that are pointed continuously at the beacon. If the interrogator scans
in space, it will not in general be pointed at the beacon during the interval
that the beacon is tuned to its frequency band unless the scanning period
is made short compared with the interval during which the beacon replies.

Some such beacons have a single tube used both as a superregenerative
receiver and as a pulsed transmitting oscillator so that by mechanical
changes of the tuning of the resonant circuit both frequencies can be
changed together. The frequency for reception and that for transmis¬
sion are nearly the same; they are not identical because of the different
voltages and transit times involved at the two different levels of operation.
Figure 8T0 shows two readily realizable cycles of variation of frequency

Sec. 8-7]

INTERROGATION CODES

263

with time. The intersections of the horizontal lines with the sawtooth
curves give the times at which replies are received by a radar tuned to the
frequency corresponding to the horizontal line. In case a all interroga¬
tors at different frequency get regularly spaced pulses, in case b they come
in pairs, the grouping depending on the frequency. This use of a single
tube for receiver and transmitter is convenient especially because it tends
to mitigate the effects of antenna mismatch often encountered in installa¬
tions in the field. The shift of frequency for both transmitter and
receiver is automatically almost exactly the same. Separate receivers
and transmitters whose tuning controls have been ganged can be used
if desired but this method requires more care in design and installation.

CODING

The simplest type of beacon replies with a single pulse to every pulse
of sufficient strength received within a certain band of frequency. For
purposes of reducing interrogation by confining it to only those interro¬
gators that are intentionally seeking beacon replies, coding of the
interrogation may be used. Likewise, the replies may be made more
complicated in a variety of ways for the purpose either of identifying
the beacon or of using it as a part of an auxiliary communication system.

8-7. Interrogation Codes. Frequency .—If the beacon is one that
replies to all radars of a given type, the frequency for interrogation is not
highly characteristic. If it is one to be used in a system with specially
designed interrogator-responsors, certain discrete interrogation fre¬
quencies can be used as part of a code characterizing the particular
beacon.

Pulse Length .—In order to avoid excess interrogation of ground
beacons by airborne radars not interested in beacon replies, some beacons
have been designed so that they are triggered only by pulses longer than
those used for ordinary radar search. Careful design of the beacon
receiver is required to prevent the stretching of strong, short pulses to
give the same effects as longer ones of medium strength, but this problem
has been solved satisfactorily. The beacon reply is obviously delayed
since it cannot occur until after the lapse of a time longer than the dura¬
tion of the search pulse. This delay must be allowed for in estimating
the range to the beacon.

Multiple Pulses .—The beacon can be made to include a decoder so
that a trigger is developed only upon reception of a pair of pulses having
the proper separation, or it can be made so that it will reply only upon
reception of a still more complicated group of properly spaced pulses.
A considerable time delay may be involved, but in many cases this can
be obviated by having the sweep of the interrogating radar started by the
last of the group of interrogating pulses. One of the principal benefits

264

RADAR BEACONS

[Sec. 8-8

to be derived by the use of this more complicated system is relative
freedom from random triggering by other radar sets in the same band since
the probability of getting such a group of pulses by accident decreases
rapidly as the complication of the group increases. This matter is dis¬
cussed more fully below. All such systems, however, are subject to some
difficulties resulting from the presence of reflected signals that are delayed
because of the longer path traversed.

Two-frequency Interrogation. —Another method related to the use of
groups of pulses is the use of coincident interrogation at two different
frequencies. The two pulses may be actually coincident, or one delayed
with respect to the other by any fixed amount. Both the value of the
second frequency and that of the delay give additional coding possibilities.

Communication by the Interrogation Link.— So far, methods of interro¬
gation coding have been discussed which determine whether or not the
beacon will reply when interrogated. More complicated schemes for
coding the interrogating beam enable the transmission of information to
the vehicle carrying the beacon. Such schemes are usually applied only
in cases where the interrogating antenna points continuously at the
beacon. Information in the telegraph code can be conveyed by turning
the interrogator on and off, by varying the width of the pulses, by chang¬
ing the spacing between pairs of them, by changing the number of pulses
in groups, and by varying the pulse repetition rate. When the repetition
rate is made high enough, the relative spacing of pairs of pulses or
the pulse width can be varied at voice frequencies to give telephonic
communication.

8-8. Reply Codes. Frequency. —Some coding can be had by use of
several spot frequencies for beacon replies.

Gap Coding. —The beacon transmitter can be turned on and off to
give Morse letters. This system is useful only when the interrogator is
expected to look at the beacon steadily. A variant that has been sug¬
gested for use with scanning radars is a rapid code of this kind which
would break the reply arc on the PPI into dots and dashes. Only simple
codes could be used because of the limitation of beamwidth and the
complete uncertainty as to the part of the coding cycle for which the
broken reply arc would be centered.

Width Coding. —Letters of the Morse code can be transmitted by
changing the width of the pulses in the proper sequence instead of turning
the pulses on and off. Beacons emitting such width-modulated replies
will give a display on scanning radars and have the additional slow gap
code which can be read if the scanning is stopped.

Range Coding. —Codes readily visible on the PPI, as in Figs. 8-2a and
8-26, are obtained by having the trigger operate a coder that causes the
emission of a number of reply pulses. These may be grouped in time in

Sec. 8-9]

TRAFFIC CAPACITY

265

different ways in order to give various groups in apparent range on the
indicator. They are instantly readable by rapidly scanning radars, but
have the disadvantage of being more subject to confusion by overlapping
patterns, when numerous beacons are present at nearly the same bearing,
than are replies that give simpler patterns.

Voice Communication .-—Here also, when the repetition rate is high
enough, the relative spacing of pairs of reply pulses or the width of pulses
can be varied at voice frequency to give telephonic communication, usable
when the interrogator-responsor points steadily at the beacon.

STATISTICAL CONSIDERATIONS

8-9. Traffic Capacity. —For every beacon there is some limit to the
total amount of energy it can radiate per second, with a corresponding
limitation of the number of its replies per second and of the number of
interrogators that can work with it simultaneously. Beacons have been
made in which the limit to the rate of reply was set by the amount of
interrogation necessary to overheat the beacon until it started a fire, but
this informal system has drawbacks. It is usually desirable to incor¬
porate an arrangement for limiting the average rate of reply to a safe
value. There are two principal ways of doing this.

In the first method, the sensitivity of the beacon receiver is decreased
as the average number of replies increases. Weaker interrogations are
thus rejected and the replies are limited to stronger interrogators up to
the maximum number tolerable. For navigational beacons, in general,
this is not a good scheme since it tends to eliminate replies to the more
distant interrogators, which are likely to be the ones most in need of
getting them. For some purposes, where beacons of short range are to
be used in connection with landing systems, this might prove to be a
useful method.

The second method involves reducing the ratio of the number of
replies to the number of interrogations to keep the total number of replies
within the safe limit. The beacon display of all interrogators is some¬
what impaired if there is sufficient overinterrogatiori to reduce this ratio
markedly, but there is no discrimination against the far-off interrogators.
This result is accomplished by varying the period of insensitivity of the
beacon following the emission of its coded reply. There is always a
finite minimum time between successive beacon replies; the maximum
number of possible replies is thus the reciprocal of this time. Usually
this maximum number is too great for safety unless the “dead” time has
deliberately been made greater than it would naturally be. The simplest
way to protect the beacon against overloading is to arrange that the
receiver will always be dead for the desired time after making a reply and
will then recover sensitivity so quickly that stronger interrogators are

26C

RADAR BEACONS

[Sec. 8 9

not favored. This simple system can lead to occasional unnecessary
interference of one interrogator with another. Let us assume, for
example, that there are but two interrogators and that the beacon could
readily reply to both steadily. If the dead time is long, there will never¬
theless be times when the interrogations from one beacon will arrive in
the dead time following the reply to the other. A more complicated sys¬
tem that avoids this defect has been used. The dead time is normally
short but is arranged to increase, as needed, with increasing average rate
of interrogation. Too short a dead time can be troublesome, for it may
lead to multiple interrogation by the same interrogator pulse that has
reached the beacon not only directly, but also by other and longer paths
involving reflection.

If W represents the probability that the beacon will reply to an inter¬
rogating pulse of sufficient strength, it is easy to show by a statistical
argument that

W >

1 + nr

(6)

and

W <

I + (n - 1 )t

(7)

In these expressions, n is the number of like interrogators having almost
equal recurrence rates, and t is the ratio of the dead time to the total
interval between interrogating pulses. Thus r is the fraction of the time
that the beacon is insensitive to a second interrogator if it is replying
fully to a first one. If the recurrence rates of the interrogators were
exactly equal, there would be a fixed phase relationship between pulses
and the statistical argument would be inapplicable. When interrogating
radars have crystal-controlled repetition rates that are almost exactly
equal, the radar that first emits its pulses may for a time steal the beacon
completely away from a second radar that emits its pulses somewhat
later. Equation (6) results from assuming complete randomness of
interrogations, and gives a result that is absurd when there is but one
interrogator. Equation (7) results when we assume that the probability
of reply to a particular pulse from one interrogator is completely unin¬
fluenced by the existence of the other interrogations by that interrogator.
This assumption is false since there is indirectly such an influence. The
exact expression for W is cumbersome but this is of little practical con¬
sequence since it need not be used. The two values obtained from Eqs.
(6) and (7) bracket the true value and differ from each other unimpor¬
tantly in practical cases. A useful approximation for W is given by

1 + in - W)t

W =

(8)

Sec. 8.9]

TRAFFIC CAPACITY

which transforms to give

Wb - W + 1
Wt

267

(9)

Figure 811 gives a plot of Eq. (9) for two values of r. For existing radars
and beacons r is ordinarily of the order of 0.1.

It is clear from the foregoing that there is no simple way to estimate
the traffic capacity of a beacon system since it depends on the lowest value
of W tolerable for satisfactory operation, and that in turn depends to a
considerable extent on the indicators of the interrogator-responsor. For
certain actual microwave radars and beacons, something like five radars
giving steady interrogations are allowable without serious impairment
of the presentation. Where necessary, this number can be increased by
designing the beacon to have a shorter dead time.

So far in this discussion, the results of scanning by the interrogating
radars have been ignored. If a
radar scans through 360° and inter¬
rogates the beacon through only 6°,
it will load the beacon only tts as
much as if it pointed at it steadily.

The traffic capacity of the beacons
in such a system is increased by a
factor of about 60. Actually, it is
necessary to take account of the
statistical fluctuations of the inter¬
rogation. Therefore, the number
of interrogating radars should be
substantially less than would be allowable if they remained uniformly
spaced in their intervals of interrogation. Interrogating planes near the
beacon tend to interrogate through much greater sectors of their scan and
thus load the beacon disproportionately. For this reason, control of the
width of the reply arcs by decreasing the interrogating power would be
desirable.

In any case, if large traffic is to be expected, it is desirable to use some
sort of interrogation coding to ensure that beacons will be triggered only
by those radar sets that want to look at them, and not by ones uninter¬
ested in getting replies from the beacon.

The effectiveness of multiple-pulse interrogation codes in cutting
down unwanted beacon replies can be seen as follows. Let us assume
that N random pulses per second are received by a beacon, and that the
beacon is triggered if any pulse is followed by a second one that arrives
later by an interval of time between D — T and D + T. D is the delay,
and ±T is the tolerance. Each pulse thus produces a following interval

pulses, W, getting replies as a function of
the number of the interrogating radar
sets, n.

268

RADAR BEACONS

[Sec. 8-10

of sensitivity to triggering by a second pulse of amount 2 T. If N pulses
arrive per second on the average, the average sensitive time per second
will be 2TN. This is also the fraction of the time that the beacon is sen¬
sitive, or the probability that a random pulse will find it sensitive and
trigger it. Since N random pulses arrive per second the number of
triggerings per second will be N times this probability, or 2TN 2 . Thus,
the ratio of the number of beacon replies to the number of random pulses
per second is 2TN. If, for example, T = 5 /nsec and N = 500 pps, the
product 2TN has a value of sirs, the number of random triggerings per
second being reduced from 500 to 2.5. If a three-pulse code is used, a
similar argument applies for the third pulse and an additional factor of
2TN will come in to give 47’ 2 A r3 as the number of random replies per
second.

The argument also applies to two-frequency interrogation. Here
the number of random interrogations will be 2TN 1 N i if A r i and ,V 2 are
the respective random rates at the two frequencies, and the beacon is
made so that the two pulses have to arrive in a certain order for trigger¬
ing to occur. If the order is immaterial, the rate of random interroga¬
tion will be twice as great, namely, ATNiNi.

In making a comparison between the two systems, it is necessary to
keep in mind that one must use estimates of the numbers of random
pulses that will be present after the system has been introduced. Chang¬
ing radar sets to give double pulses increases the number at the radar
frequency; adding coincident interrogating pulses at a second frequency
increases the number at that frequency.

8T0. Unsynchronized Replies.—When a beacon is being interrogated
by several radars at the same time it replies to all, and the receiver of each
interrogator-responsor will respond to all of these signals. Replies to the
interrogation by a particular radar are synchronized and give a stationary
pattern on its indicator as do its radar echoes; the replies to interrogations
by the other radar sets appear to be unsynchronized and thus show at
random on the screen and are similar to random noise from other causes.
Figure 8T2 shows several beacon signals appearing on the PPI of a 3-cm
radar; one of them is sufficiently overinterrogated to show unsynchronized
replies. This effect is displeasing aesthetically, but experience has shown
that a great amount of overinterrogation is necessary to interfere seriously
with recognition of the beacon. The problem is more troublesome when
numerous adjacent ground or ship interrogators are interrogating nu¬
merous airborne beacons. Unsynchronized replies coming from the multi¬
ple interrogation of a near-by beacon may interfere with detection of the
signals from one farther away at the same azimuth. It is difficult to
make a definite statement about the extent of the interference because it
depends so much on the characteristics of the radar set. The use of

Sec. 8-10]

UNSYNCHRONIZED REPLIES

269

delayed fast sweeps is helpful since the density of random signals on any
region of the scope is thereby reduced. Also, fewer unsynchronized
replies are encountered when narrow-beam, scanning radars are used since
the chance that several radars will be looking at a given beacon at the

»,v.

Fig. 8-12.—Four 3-cm beacons on the scope of a plane flying over England.

Beacon at 50° (Beachy Head)

Beacon at 180° (Defford)

Beacon at 280° (Alconbury)

Beacon at 340° (Halesworth)

The Alconbury beacon shows numerous unsynchronized replies resulting from interrogation
by other radar sets.

same time is reduced. This trouble is mitigated (as is the one of over¬
interrogation of a particular beacon) by all arrangements that help in
avoiding interrogation of beacons except when the beacon replies are
wanted.

In systems that use crystal oscillators for accurate measurement of

270

RADAR BEACONS

[Sec. 8-10

range and incidental fixing of pulse repetition rate, the replies to interro¬
gations from a given interrogator may appear as signals from a false
beacon on the indicator of a second set because the two repetition rates
are almost exactly equal. In two such systems used in the past war, it
was found necessary to jitter the timing of the interrogation by whole
numbers of periods of the crystal in somewhat random fashion in order to
avoid this effect and the associated difficulty already mentioned—that of
possible “stealing” of the beacon by one interrogator.

CHAPTER 9

ANTENNAS, SCANNERS, AND STABILIZATION

By W. M. Cady, C. V. Robinson, F. B. Lincoln, and
F. J. Mehringer

The antenna is the sensory organ of the radar set. Its function is to
accept r-f energy from the transmission line, to distribute this energy into
space as desired, to gather in the radar echoes of this energy, and to direct
these echoes back into the transmission line. Since the nature of elec¬
tromagnetic radiation is such that a good transmitting antenna is also a
good receiving antenna, we need consider only the former function. In
most cases the antenna is required to form the energy into a sharp beam
which may be aimed in various directions. The supporting structure is
known as the “pedestal,” and the entire assembly is termed the “antenna
mount” or “scanner.” 1 Airplanes and ships are notoriously unsteady
vehicles, whose motions disturb the direction of a radar beam of energy
transmitted from them. The compensation for such motions is called
“stabilization.”

9T. The Antenna Equation. 2 —Two of the salient requirements of
most radar sets are that they be able to reveal distant objects and be able
to give accurately the direction of such objects. The design of the
antenna has a great influence on the attainment of these requirements.
We have seen (Sec. 21) that under certain conditions the maximum range
of detection of a given target varies as the square root of the area of the
antenna. This is one reason for the use of large antennas. Another
advantage of large antennas, having to do with the resolution of the radar
set, is that the beamwidth varies inversely as the linear dimension of the
antenna. Mathematically the beamwidth 9 (degrees) is usually related
to the width D of the antenna and the wavelength X of the radiation by
the approximate formula

e « 70 A, (i)

if D and X are measured in the same units. We see that shorter wave¬
lengths make possible sharper beams; this accounts for the very con-

1 For a fuller account of radar scanners the reader is referred to Radar Scanners
end Radomes , Vol. 26 of this series.

2 Secs. 91 to 912 by W. M. Cady.

271

272

ANTENNAS, SCANNERS, AND STABILIZATION

[Sec. 9-2

spicuous trend toward shorter wavelengths which has characterized radar
ever since its earliest development.

In the course o developing and testing a new antenna, the distribu¬
tion of the energy in the beam may be expressed by means of a polar
diagram or antenna pattern. Figure 91 displays such a pattern and

FiO. 91.—A typical antenna pattern showing the main beam of width 9 and the side lobes.

shows that the beamwidth 0 is the full beamwidth at half power. A
small amount of power is unavoidably radiated in undesired directions,
forming the “side lobes” shown in this figure.

9 2. Round and Cut Paraboloid Antennas. —One very common type
of microwave radar antenna takes the form of a paraboloidal reflector 1
with a source of radiation, or “antenna feed,” at its focus. Since the

wavelength of the radiation is short in com¬
parison with the dimensions of the reflector, it
is profitable in an introductory discussion to
regard the operation of the antenna as a prob¬
lem in ray optics (Fig. 9-2). Figure 9-2 does
not explain the side lobes or the beamwidth,
but it does serve to emphasize the fact that
the feed is always so designed as to be directive.
Figure 9 3 represents an automatic record of
the energy radiated at various angles from a
well-designed feed, the directional power being
displayed as a function of angle. It is obvious
that nearly all of the energy from the feed will
strike a properly placed paraboloid, which will
then collimate the radiation. Figure 9-4
shows the radiation from an incorrectly designed feed. A correct design,
used in the 3-cm band, is illustrated in Fig. 9-5, which shows two dipoles
excited by the radiation field from the y- by 1-in. waveguide transmission
line. The dipoles are so adjusted in length and position that their com¬
bined effect is to direct the radiation back within a cone surrounding the
line without reflecting radiation into the waveguide.

Equation (1) requires further comment in the case of a paraboloid
reflector of which the perimeter has been so trimmed (“cut paraboloid”)
that its width and height are unequal. If the beam is pointed horizon-

1 The subject of paraboloid and other types of antennas is developed in Microwave
Antenna Theory and Design, Vol. 12 of this series.

Fig. 9-2.—Ray diagram of a
paraboloid antenna.

Sec. 9-21

ROUND AND CUT PARABOLOID ANTENNAS

273

Fig. 9-4. —The angular distribution of energy from a two-dipole feed incorrectly designed.

274

ANTENNAS, SCANNERS , AND STABILIZATION

[Sec. 9-3

tally, the beamwidth can be measured by exploring the intensity of the
radiation to the right and left of the center of the beam or, alternatively,
above and below the center of the beam. It is an important fact that
the beamwidth as measured vertically depends, according to Eq. (1), upon
the vertical dimension of the cut paraboloid, and the horizontal beam-
width depends upon the horizontal dimension. Thus, in order to realize
high resolution in azimuth, the antenna must be wide but not necessarily
tall, whereas a height-finding radar, affording accurate measurement of
the angular elevation of an airplane, must have a tall antenna which need
not be wide. These two types are exemplified by the scanners shown
in Figs. 9-15 and 9T4 respectively.

We have not mentioned the “mattress” type of antenna, which is
perhaps the most familiar to the public because it is commonly seen on
naval ships. These antennas are rectangular arrays of radiating elements
so phased as to produce a broadside beam. They are widely used in
radars of wavelength over 1 m. With the trend toward shorter wave¬
length, the mattress antennas are giving way to the types discussed above.

9-3. Fan Beams. —One of the functions for which airborne radars are
designed is aiding air navigation, and an extremely important type of
airborne navigational radar presents a map of the terrain around the
aircraft. In order to map the ground the transmitted energy must be
directed toward the ground, and rather than having the energy beamed
like a searchlight, a “fan beam” must be employed as shown in Fig. 9-6
for complete coverage. A uniformly intense map is desired, which will
display ground objects that lie at depression angles between, for example,
5° and 70° below the horizontal. The energy in the fan beam must there¬
fore be properly distributed to give adequate illumination of the most
distant objects while not overilluminating those which are at greater
depression angles. It can be shown, subject to certain simplifying
assumptions, that the energy should be distributed as the square of the
cosecant of the depression angle (see Sec. 2-5). Figure 9-7 shows how
well such a pattern is realized in practice, with an antenna 12 in. in height
(shown in Fig. 9-8) used at the 3-cm band. In this polar diagram the
square root of the power is plotted rather than the power itself, since the
desired distribution is then given by a straight line as shown. Figure 9-9
is a photograph of the PPI display, showing the performance of this
antenna.

Sec. 9-3]

FAN BEAMS

275

The cosecant-squared fan beam is used not only in airborne naviga¬
tional radar but also in surface-based radar for the detection of airplanes.
In this case the fan is inverted, the intention being that a target airplane

Fio. 9-6.—A fan beam which enables an airborne radar to scan the surface of the earth.

10 °

90° 80° 70° 60" 50° 40° 30° 20’

Fig. 9-7.—The energy distribution to a square-root scale as a function of the depression
angle in an airborne navigational radar.

flying at any constant altitude will be indicated with a constant intensity,
independent of range.

Several antenna types have been developed for producing a cosecant-
squared fan beam; those most widely used can be discussed in terms of

276

ANTENNAS , SCANNERS, AND STABILIZATION [Sec. 9-3

ray optics. Figure 9-10 shows two distortions of a paraboloid used for
this purpose. Another widely used method employs a cylindrical reflector,
shaped like the blade of a snowplow or bulldozer, and having only single
curvature (Fig. 9-8). Such a reflector is illuminated by the radiation
from a linear feed rather than a point feed. In this case the linear feed
defines the beam sharpness in regard to azimuth and the reflector dis¬
tributes the energy in elevation. The ray diagram shown in Fig. 910a
will serve again to illustrate the formation of the cosecant-squared fan.

Support from wing spar Elevation motor

Reflector

Fig. 9-8.—A scanner with a 60-in. shaped cylindrical reflector, ventrally installed in a B-29.

In this figure the linear feed is imagined perpendicular to the plane of the
drawing. The feed is frequently the straight opening between two
identical parallel conducting sheets which are joined along their curved
backs by a parabolic reflector strip. Just inside the center of the opening,
at the focus of the parabolic strip, is located the open end of a waveguide
which irradiates the parabola, thereby setting up the propagation of
energy between the two sheets and straight out through the opening.
This assembly is called a “pillbox.” Microwaves may be propagated
between the sheets with the electric field polarized either parallel or
perpendicular to the sheets. In parallel polarization the spacing must be
held accurately in order to prevent distortions of the wavefronts; slender
spacing posts are used since they have almost no effect on the waves. In

Sec. 9-4]

NONSCANNING ANTENNAS

277

perpendicular polarization, posts scatter the radiation badly and are not
generally used; but fortunately the wavefronts are not disturbed by
gentle variations in the spacing of the sheets. Both polarizations are
used in practice.

Fig. 9-9.— Photograph o/ PPI scope of 3-cm airborne radar: Cape Cod area.

Another type of linear source of radiation is the linear array of dipoles.
If these are so excited as to emit energy in phase, the resulting radiation
is a fan in the broadside direction. Further discussion of line sources of
radiation will be found in Secs. 912 and 9-14.

9-4. Nonscanning Antennas. —There are certain types of radar
antenna which are not ordinarily required to scan. In this category are
the end-fire antennas which are sometimes attached to airborne guns in
order to permit radar range-finding. As an example, one end-fire linear
array (Fig. 911) is a series of dipoles excited in such a phase relationship
that their energy is beamed in the direction of the array. Another end-
fire array is the Yagi antenna. Commonly, this is an array of dipoles,
only one of which is excited by the transmission line; behind it is a para¬
sitic reflector dipole and in front are several parasitic director dipoles. The

278

ANTENNAS, SCANNERS, AND STABILIZATION [Sec. 9 4

Yagi array has been widely used for wavelengths of several decimeters;
an example is shown in Fig. 6-30. An end-fire antenna can also consist
of a polyrod (a rod of polystyrene) of appropriate dimensions, into one end

(a)

( 6 )

Fio. 9-10.—A paraboloid reflector may be distorted in various ways in order to produce a

fan beam.

Fiq. 9*11.—An end-fire array and its housing for use in the 10-cm band.

of which r-f energy is introduced. These end-fire antennas are useful
in cases where a paraboloid would obstruct vision or add unduly to the
aerodynamic drag of an airplane. An array of 42 polyrods, placed
parallel and excited in phase, has been used as a broadside array as shown
later in Fig. 9-32.

Sec. 9-5]

CONSTRUCTION OF RADAR ANTENNAS

279

Beacon antennas are often made up of a vertical array of radiating
elements excited in phase. By correct design of such an antenna the
pattern can be made reasonably uniform in azimuth and at the same time
well confined to the region of the horizon. Like other beacon antennas,
the antennas used for IFF equipment are not strictly radar equipment
and will not be discussed. The same statement applies to the antennas
used in the search and jamming functions of radar countermeasures.

9-6. Construction of Radar Antennas. —The main requirements in the
mechanical construction of airborne antennas are accuracy of form, the
ability to withstand field service conditions, and light weight. Surface-
based antennas must be no less accurate, and considerations of weight,
inertia, and wind forces are paramount. Considerable advances have
been made in the mechanical design of airborne, and particularly of sur¬
face-based, antennas for microwave radar during the recent war. In
this section only antennas in which the feed is distinct from the reflector
are considered; array antennas are not discussed.

Sheet aluminum or magnesium alloy is always used for the airborne
reflectors. Small reflectors up to 30 in. in diameter are simply spun or
otherwise formed, a bead around the rim being added for stiffness, as in
Fig. 9T7. The tolerance allowable in the surface of the reflector is about
of a wavelength.

The larger sizes of airborne reflectors, whether paraboloid or shaped
cylindrical surfaces, thus far installed in a streamlined airplane are con¬
siderably wider than high and are used for circular scanning. On these
it is good practice to use aircraft construction methods. The selection of
materials used depends upon the size of the reflector and the stresses
involved. Magnesium or aluminum alloy will serve for airborne equip¬
ment. Since aluminum alloy has better forming characteristics than
magnesium, it is considered the best material for the reflector face. The
most accurate method of forming aluminum alloy sheet for the reflector
face is by stretching the material over a metal die which has been cast
and ground to the desired contour; these dies are usually made from
Kirksite, a lead and zinc alloy. After forming, the sheet metal conforms
to the exact contour of the die providing the draw is shallow enough, as is
the case with most radar reflectors. The next problem is to support this
reflector face rigidly and to maintain the contour already obtained by
forming. This can be done, as in the 5-ft reflector of AN/APQ-13 shown
in Fig. 9-8, by riveting to the rear surface of the reflector several stamped
or machined ribs contoured thereto and boxing in by riveting another
sheet of aluminum or magnesium alloy across the back; flush rivets are
preferable on the front face. A 42- by 10-in. reflector with single curva¬
ture can be made within a tolerance of +0.005 in.

In the case of a large reflector, over 5 ft in width, weight may be saved

280

ANTENNAS, SCANNERS, AND STABILIZATION [Sec. 9 5

by using sheet-metal ribs or channels formed by the hydropress method,
and boxed in at the rear as in Fig. 9-8, or by using a stamped outer frame
made by the drop-hammer method, as in the 8-ft reflector shown in
Fig. 9-12. These waffle-shaped frames require no ribs for stiffening
because the mating section conforms to the contour of the back of the
reflector face. An aluminum-alloy supporting bracket can be riveted to

RADAR SCANNING PATTERNS

We have seen that although a few radars have been designed with
radiation beams that are fixed in direction, the great majority of radar
beams are made to scan. The motion of the beam may be thought of as
the motion of a point on a sphere that is centered at the scanner. The
beam sweeps over a certain region on the sphere determined by the opera¬
tional function of the radar; often it does so periodically, and in a set
geometrical pattern termed the “scan.” The great variety of scans may
be divided into two categories, simple and complex. A simple scan is one

Fig. 9-12.—Rear view showing the construction of an 8-ft airborne paraboloid trimmed to a

3-ft height.

the structure; or, if the elevation angle of the beam must be adjustable,
the ends of the structure may be supported by ball-bearing trunnions.

Surface-based antennas are usually not housed, and therefore are
subject to wind forces. These forces can be reduced by as much as 50
per cent if the reflector is a grille (Figs. 9-14 and 9-28) or a perforated
sheet (Fig. 9T3). Fortunately such perforation does not impair the
electrical performance if the holes are not larger than about one-eighth
wavelength in the direction of the magnetic vector.

Sec. 9 - 7 ]

COMPLEX SCANS

281

in which the beam sweeps with but one degree of freedom, that is, it
covers repeatedly one and the same arc on the sphere. A radar employ¬
ing a simple scan can tell the range of a target and only one of its angular
coordinates, e.g., azimuth. In a complex scan the beam ranges over a
certain solid angle, by virtue of possessing two degrees of freedom. A
radar possessing a complex scan can tell the location of a target in space
by giving the range and two angular coordinates, e.g., elevation and
azimuth.

9-6. Simple Scans. —One of the simple scans in common use is the
circular (or “horizon,” or “all around looking,” or “360°,” or “A”) scan;
the beam travels continuously around the horizon, or may be adjusted to
scan around at any constant angle above or below the horizontal. This
scan is widely used in radars providing surface-based surveillance of land,
vessels, and distant aircraft; and it is used (see Fig. 9-6) in airborne radar,
serving, for instance, as an aid to air navigation. In certain scanners
the beam can be adjusted to a position above or below the horizon at the
will of the operator. The scan rate is usually in the range between 4
rpm for large scanners and 30 rpm for small. Sector (or “B”) scan is a
modification of circular scan in which the beam scans to and fro on an
arc. This motion is common in certain airborne radars for surface search.
The sector is typically 75° wide, and 1 to-and-fro cycle may occupy 1 sec.
The third simple motion of the beam is conical scan, in which the path
described on the sphere is a circle of a very few degrees diameter. This
scan is not used for search, but finds wide use in accurate tracking of an
individual target (see Sec. 6T4). The diameter of the circle described
by the center of the beam is chosen with this application in mind; it is
commonly such that the intensity radiated to the center of the circle is
somewhat greater than half the peak intensity. The scan rate is usually
at least 1200 rpm.

9-7. Complex Scans. —A radar having spiral scan was used in single¬
seat nightfighter aircraft during World War II. This complex scan may
be described as a conical scan in which the angular diameter of the circle
described by the beam is continuously varied from 0° to a maximum of,
for example, 60° and back to 0°. By this motion the solid angle covered
is scanned completely in, say, 1 sec as the beam spirals outward.

A helically scanning radar was used in nightfighters that carried a
radar operator in addition to the pilot. The beam revolves rapidly
around a vertical axis, as in horizon scan, while the elevation angle is
made to oscillate much more slowly between limits a few degrees above
and below the horizon. In this way targets may be sought within a hori¬
zontal 360° zone except for whatever blanking is caused by the structure
of the nightfighter itself. The time required to explore this zone is
approximately 3 sec.

A marriage of the horizon scan (or, alternatively, the sector scan)

282

ANTENNAS, SCANNERS, AND STABILIZATION [Sec. 9 8

with the conical scan produces the Palmer scan, the cycloidal motion of
the beam which results when a conical scanner slowly traverses the hori¬
zon. The region of search is a horizontal rectangle with semicircular
ends. Palmer scan was used to accomplish an easy transition from the
search function to the gunlaying function of a fire-control radar. The
name derives from a familiar exercise in the Palmer system of calligraphy.

Other complex scans have been used mainly in experimental equip¬
ment. Probably the most useful of these is a scan in which the elevation
(or azimuth) angle oscillates rapidly while the azimuth (or elevation)
angle oscillates slowly.

MECHANICAL SCANNERS

In most cases the entire radar antenna is put through certain angular
motions in order to make the beam scan. The antenna assembly, includ¬
ing the mount that supports it and makes it move, is called a “mechanical
scanner.” The t6rm “electrical scanner” is reserved for cases where the
beam is moved not by a motion of the antenna as a whole, but rather by
relatively subtle motions of the feed or other parts of the antenna. The
borderline between mechanical and electrical scanning is not well defined.
For instance, in denial of the foregoing definitions, the mechanical
category includes the conical scans that are mechanized by the circular
motion of a point feed around the focus of a fixed paraboloid. An electri¬
cal scan is frequently used to produce a rapid sector scan of small angular
amplitude.

9-8. The Kinematics of Mechanical Scanners. —The intended use of
a radar fixes the type of scan, and the type of scan fixes in turn the
kinematic aspects of the scanner design. A circular scan is mechanized
by simply revolving the antenna on a horizontal turntable. If it is
desired to raise or lower the beam, the turntable must carry bearings so
that the antenna may be tilted about a horizontal axis at right angles to
the beam; the scanner may be described as a tilting antenna on a rotating
assembly on a fixed base. Airborne scanners of this type are usually
mounted on the under side of the fuselage, the antenna being below the
pedestal. Sector scanners are kinematically similar to circular scanners.

To enable the radar operator to control the antenna from a distance
the tilting is usually actuated by a motor. This motor may be located
on the turntable (in which case it must be powered through slip rings) or
else on the base (in which case a special mechanism must be provided for
transferring the mechanical power from the tilt motor to the revolving
antenna). Both methods are used in practice although only the former
is encountered in surface radars.

Conical scan may be effected by spinning the antenna about an axis
not quite parallel to the beam (AN/APS-6, Fig. 9-17); or by spinning the

Sec. 9-101

R-F TRANSMISSION LINES

283

paraboloid about an axis passing through the feed, the paraboloid being a
few degrees “drunk ” in relation to this axis (AN/APG-15); or by spinning
an electrically asymmetrical feed about the axis of the fixed paraboloid
(SCR-584, Fig. 9-13). All these methods and others are in wide use.

Of the complex motions, the spiral scan has been mentioned as
derived from conical scan, and more particularly from three varieties
just listed. This is exemplified in the first two cases by the Navy’s
AN/APS-6 nightfighter radar and the British AI Mark VIII. Helical
scan is used in the SCR-720 Army AI radar and in the SCR-584 anti¬
aircraft set. In the latter a conical scan is superimposed so that the
result is a sort of helical Palmer scan.

9-9. The Weight of Mechanical Scanners. —The design of a mechani¬
cal scanner is largely dependent on its antenna. Although only a small
percentage of the scanner weight is attributable to the antenna, a large
antenna necessitates a heavy scanner. Airborne scanners show this
relation very strongly. A survey of weights 1 indicates that, very roughly,
the weight of scanners having simple scans is given by 0.09D 2 pounds,
where D is the paraboloid diameter in inches. The formula for complex
scans is 0.13/T. The survey shows that among airborne radars with
mechanical scanners the scanner weighs 13 to 106 lb, representing from
6 to 21 per cent of the weight of the set, with an average of about 14 per
cent. Surface-based scanners are in general larger than airborne scan¬
ners. The weight runs from 75 to 5500 lb in shipborne antenna mounts,
and as high as 28,000 lb for land-based. The antenna mounts of surface-
based radars represent 10 to 40 per cent of the total weight of the set.

9T0. R-f Transmission Lines. —The r-f energy generated at the
transmitter is radiated by the antenna, and the echo is led back from the
same antenna to the mixer. The same transmission line 2 is used for both
the transmitted and the received energy. A rotary joint must be inserted
in the line whenever more than a few degrees of rotation of an antenna
are required. Such a joint is always installed with its axis coinciding
with the axis of the corresponding degree of freedom. Pressurization of
the rotary joints, when necessary, is accomplished either by means of a
composition rubber ring revolving snugly around a polished steel tube, or
by means of a polished carbon ring revolving in contact with a polished
steel annulus. Helical scanners have at least two rotary joints, i.e..
for azimuth and elevation, as have spiral scanners.

9-11. Data Transmission. —The continuous transmission of informa¬
tion from the scanner to the indicator, giving the attitude of the antenna
in relation to its base, is known as “data transmission.” Often these

1 W. L. Myers, USXR, “Weight Analysis of Airborne Radar Sets,” RL Report
No. 450, Jan. 1, 1945.

2 Chap. 11 contains a discussion of the transmission line and associated components.

284

ANTENNAS, SCANNERS, AND STABILIZATION [Sec. 912

data are transmitted as voltages induced in synchros. 1 There is, for
instance, a synchro generator built into the AN/APQ-13 scanner shown
in Fig. 9 8 which revolves 10 times for each azimuth revolution of the
antenna; a synchro motor in the indicator imitates the motion of the
generator, and through a gear reduction rotates the deflection coils of
the PPI in synchronism with the antenna. Occasionally a potentiometer
or a sine-wave generator is used as the data-transmitting element. A
similar type of data transmission is required of servo-controlled scanners:
a voltage from the transmitting element is compared with a voltage from
the knob, etc., that is to control the antenna, and the antenna is auto¬
matically driven in the direction w'hich will bring the error signal or
difference voltage to zero.

9T2. Examples of Mechanical Scanners.- —The above generalities
will be made more concrete in the description of a few specific scanners.
These are chosen to illustrate a variety of purposes, shapes, and sizes.

The SCR-58A .—The antenna mount of the SCR-584 (Fig. 9-13) has
been cited as a Palmer scanner, inasmuch as it combines helical with
conical scan. The prime function of this radar, 2 located in a trailer, is
to locate enemy aircraft and to provide an antiaircraft director with data
on slant range, azimuth, and elevation angle of aircraft. The beam (at
the 10-cm band, about 4° wide) is formed by a 6-ft stamped paraboloid
illuminated by an electrically offset dipole. This 120-lb reflector is
perforated with 6400 half-inch holes to reduce weight and windage. A
gear train in the base actuates the searching in azimuth at 6 rpm. A
similar gear train is located behind the reflector and actuates the eleva¬
tion motion; the excursion in elevation is covered once per minute. To
enable tracking, the electrically asymmetrical dipole feed spins at 1800
rpm, thus scanning the beam conically; this has the incidental effect of
gyrating the plane of polarization of the energy. Five units, driven by a
spring-loaded gear train, are provided for azimuth data transmission:
four synchros, of which one is geared to rotate at 16-speed, and one
potentiometer. As is common practice in data transmission, each take¬
off may be individually adjusted by loosening its mounting clamps and
rotating the stator case for proper angular setting in relation to the
antenna. After the eventual removal of the SCR-584 radar to a new site,
any necessary reorientation of the take-offs may be effected by an
ingenious “group adjustment” of the data gear train. Units analogous
to all but one of the azimuth synchros are geared to the elevation mech¬
anism. The phase of the conical scan is continuously signaled by means

1 Potentiometers and synchros are discussed in Chaps. 8 and 10 of Components
Handbook, Vol. 17 of this series.

* War Department Technical Manual TM-1524.

Reflector

/ assembly
R-f line

V Reflector
A support"

Ik T ele J

scope 4
fflaln ountl

r Elevation
jynchro geai
housing ""

[Elevation yoke'

k Azimuth j
pedestal

L Azimuth j

drive motor

16X azimuth.

transmitting

synchro

■

s Azimuth
planetary
gears

K Azimuth drive pinion
Azimuth oil reservoir

rimuth potentiomete^
’imuth main drive gear

Azimuth synchro
adjusting handle

Azimpth

Elevat

Eevat

Azim

Slip f

Azimi

driv

Fig. 9*13.—The SCR-584 antiaircraft antenna mount with 6-ft reflector. (Courtesy of Chrysler Corporation.)

Sec. 9-12] EXAMPLES OF MECHANICAL SCANNERS 285

Fig. 914.—The AN/TPS-10 height-finding antenna mount with a reflector 10 ft high.

elevation shaft, where a second rotary joint is provided; and then into
the reflector at its vertex, where it passes through the hollow shaft of the
sine generator, a high-speed rotary joint, and the hollow shaft of the spin
motor. In order to exclude moisture, the entire line, including the three
rotary joints and the feed, is pressurized to about 5 lb/in. 2 The mount,
weighing some 2200 lb, is installed on an elevator in the trailer and so may
be raised for use or lowered into the trailer for stowage.

The AN/TPS-10 .—A second antenna mount of interest is that of
AN/TPS-10 1 (Fig. 9-14), a radar intended for detecting airplanes and
determining their altitude, especially in mountainous terrain. Although

1 War Department Technical Manual TM 11-1568.

Sec. 912]

EXAMPLES OF MECHANICAL SCANNERS

287

it may be mounted and used on two trucks, this set is more commonly
based on the ground. As mobility requires, the mount is easily assembled
and disassembled in the field, and only four of its parts exceed 80 lb in
weight.

The antenna, a paraboloid made of a grid of curved J4-in. tubes, is
trimmed to an oval contour 10 ft high by 3 ft wide. The beam is there¬
fore of a “beavertail ” shape and since the radiation is at the 3-cm band,
the beam is 2.3° wide in azimuth and 0.7° wide in elevation. The polar¬
ization is vertical. In the height-finding function the beam scans in
elevation between 2° below and 23° above the horizontal at a manually
controlled azimuth. For search purposes the azimuth motion may be
motor-driven at 4° per sec, either boxing the compass or scanning a sector.
This azimuth rate cannot be exceeded if successive sweeps in elevation are
to cover without gaps all portions of the zone being scanned. The
“oscillating beavertail” scan which results is, however, rather slow for
search, and this function is sometimes relegated to another set with which
the AN/TPS-10 may form a team.

The main bearing of the mount is a roller-ring bearing, defining the
vertical axis of the pedestal. On the turntable are mounted the antenna
and the elevation drive, consisting of motor, gear reduction, crank, and
connecting rod. The turntable also supports the pressurized modulator
and its controls, the pressurized r-f head, and the power supply for
the receiver. The r-f head is so mounted in order to eliminate the
need for an azimuth rotary joint, and the other components named are
so mounted in order to reduce the number of slip rings on the azimuth
axis. «

Long Range Ground Radar. The system now to be described was
designed for microwave early warning and surveillance of enemy aircraft
and the control of friendly aircraft. Two antennas (Fig. 9T5), usually
back-to-back on a single mount, characterize this set. One is for long-
range low-angle coverage and the other, radiating a fan beam, covers
higher elevations. The set can detect single heavy bombers to above
30,000-ft altitude and 200-mile range, provided the aircraft are above the
horizon. The antennas are similar in that each has a shaped cylindrical
reflector 25 ft long, in 11 sections, fed by a linear array of dipoles at the 10-
cm band and forming a beam 0.9° wide in azimuth. The waveguide trans¬
mission line is weatherproof, the array being housed in a Plexiglas cover.
The antennas are different in that the low-angle reflector is 8 ft high and
parabolic in vertical section, its radiation vertically polarized; whereas
the high-angle reflector is 5 ft high, of an empirically determined shape
producing an approximately cosecant-squared beam, and its radiation
horizontally polarized.

The reflectors are not perforated for the reason that the small amount

288

ANTENNAS, SCANNERS, AND STABILIZATION [Sec. 9 12

of energy which would penetrate straight through would still be focused
in azimuth and so would cause spurious signals. A solid construction is
therefore typical of shaped cylindrical reflectors. Paraboloid reflectors
need not be solid, since the radiation leaking through them from the point
antenna feed is not focused and cannot cause sharply defined false echoes.

The antennas rotate about a \ertical axis at 2 or 4 rpm, together with
their respective transmitters and common modulator. There is no ele-

Fig. 9-15.—Long-range microwave antenna mount with two 25-ft cylindrical reflectors.

-High-angle reflector
Low-angle reflector
Transmission lines
Linear arrays

for electronic units

vation control of the beam except for initial adjustment at the time of
assembling in the field. No r-f rotary joints are necessary in the wave¬
guide transmission lines. Slip rings are required around the azimuth
axis in order to carry 60-cps power, control voltages, and video signals.

Although weighing 6 tons, the ground-based version of this mount
can be disassembled and stowed on trucks in 4 hr. The truck-mounted
version is illustrated. The mount has operated in winds up to 80 mph,
and the design is such that 125-mph winds should not cause damage.

The AN/APS-10 .—In spectacular contrast with the foregoing is the
more recent of two alternative scanner designs for the AN/APS-10
navigational radar (Fig. 9-16); it is airborne and weighs about 13 lb.
The antenna is a paraboloid 18 in. in diameter, fed at the 3-cm band by a

EXAMPLES OF MECHANICAL SCANNERS

horizontally polarized dipole feed (ef. Fig. 9-5) at its focus. The beam-
width in azimuth is about 5°. The lower portion of the paraboloid is
distorted as in Fig. 9-106, so as to reflect a portion of the energy downward

paraboloid

Fig. 916.—The AN/APS-10 airborne navigation scanner with an 18-in. reflector. (Courtesy

Houston Corporation.)

to illuminate the foreground. This fan beam is approximately cosecant-
squared between 5° and 30° depression angle when the antenna is at its
normal attitude. In order to raise or lower the beam the radar operator
may tilt the antenna up or down a few degrees at will by energizing a
small motor, contained within the scanner base, which pulls a light steel
cable attached to the reflector. The waveguide transmission line is

290

ANTENNAS, SCANNERS, AND STABILIZATION [Sec. 9-12

Waveguide pump

A. A

support

reflector

connection

(covered)

Right support trunnion

■ .Vi.•

This member spins and nods

pressurized all the way from the transmitter-receiver unit through a
flexible section to the scanner, the azimuth rotary joint, and the tilt
joint to the feed, which is enclosed in a hollow Styralloy ball. Parts of
the waveguide are made of nickel electrodeposited on a die-cast form
which is subsequently melted out. The scan is circular, at 30 rpm.

Antenna feed
and

counterweight

Fig. 9-17.—The AN/APS-6 spiral scanner. (Courtesy of Dalmo Victor Manufacturing Com¬
pany.)

This scanner has an unusual feature which allows the main axis to be
adjusted to a vertical attitude despite changes in the angle of attack of
the airplane. This pitch adjustment is electrically driven and remotely
controlled by hand. A second unusual feature is the nature of the r-f
elevation joint, which allows the beam to be raised or depressed from its
normal attitude. This is merely a choke-to-flange coupling, similar to
the rigid coupling commonly employed (see Sec. 11-3), except that the
flange is slightly beveled so as to allow +9° relative motion. This
“wobble joint” is enclosed in a flexible airtight tube.

The AN/APS-6 .—The AN/APS-6 system imposes unusual require¬
ments on the scanner (Fig. 9T7). This radar is used for airborne detec¬
tion of aircraft under blind conditions, and therefore requires a search
over a solid angle in the forward direction. The beamwidth is about 5°.

The scan is spiral, and one turn of the spiral is described in sec,
which causes the plane of polarization to gyrate at this speed. The beam
is made to spiral outward from 0° (straight ahead) to 60° and back again
in 2 sec by the nodding of the antenna in relation to the yoke which forms
the forward end of the horizontal main shaft. By throwing a switch the

Sec. 9-13]

THE AN/APQ-7 (EAGLE) SCANNER

291

operator can halt the nodding of the antenna, which then executes a
conical scan to permit accurate homing. A single motor, rated at 600
watts mechanical output, provides power for the nod and spin motions.
The data take-offs are a 2-phase sine-wave generator for the spin angle
and a potentiometer for the nod angle, both being mounted on the main
gear case to obviate the need of slip rings. The gear case is unusual in
airborne practice in that it is oil-filled. Two r-f rotary j oints are required,
one on the spin axis and one on the nod axis.

A difficult problem in dynamic balance is presented by this scanner.
The difficulty arises from the fact that the fast (1200-rpm) rotor must
be in good balance for all attitudes of the antenna which is supported
thereon. In order to effect balance a special procedure has been evolved
whereby the correct number of standard lead weights may be attached
to each of eighteen points provided on the antenna and the main shaft.
A special type of balancing machine has been produced for this purpose.

ELECTRICAL SCANNERS

By C. V. Robinson

No radically new principles are embodied in the mechanical scanners
discussed in the previous section. By contrast, the electrical scanners
to be discussed in the following sections have many novel features of
fundamental design and so merit a more thorough discussion.

9-13. The AN/APQ-7 (Eagle) Scanner.— The AN/APQ-7 (Eagle)
high-resolution navigation and bombing equipment was developed at
Radiation Laboratory; Bell Telephone Laboratories carried through the
production engineering. 1

The antenna developed for this equipment produces at the 3-cm band
a horizontally polarized beam of radiation which has a width of 0.4° to
0.5° in azimuth and is shaped in elevation to give an approximately
cosecant-squared coverage down to 70° angle of depression. The beam
scans a 60° azimuth sector in -f sec, or 1 to-and-fro cycle in H sec. The
range of the Eagle system for ground-mapping is about 50 miles.

The antenna is a slender linear array 16 ft long, which fits into a
streamlined housing (vane) hung laterally beneath the aircraft that uses
it (Fig. 9T8). The body of the array consists of a fixed 16-ft extruded
aluminum channel and a movable 16-ft aluminum plate which together
form a guide of variable width (Fig. 9T9). A row of 250 dipole radiators
is mounted in the fixed channel in such a way as to draw power from the
guide formed by the two long aluminum members. A mechanism varies

1 L. W. Alvarez, “Microwave Linear Radiators,” RL Report Xo. 366, June 30,
1942; R. M. Robertson, “Variable Width Waveguide Scanners for Eagle and GCA,”
RL Report Xo. 840, April 30, 1946.

292

ANTENNAS, SCANNERS, AND STABILIZATION [Sec. 913

the guide width (and thereby the wavelength in the guide) 1 periodically;
this, in turn, varies the effective dipole phasing and moves the beam in
azimuth.

Fiu. !M8.—AN/APQ-7 antenna housing on a B-24.

Fig. 9-19—View of AN/APQ-7 scanner showing dipoles.

If all the dipoles are excited in the same phase, the beam is broadside
to the array and directed straight ahead of the aircraft. With the dipole
spacing actually used, this occurs when the inside width a of the guide
is 1.200 in. Let us assume that the energy is propagated in the wave¬
guide from left to right. Then, as the guide is narrowed to 0.660 in.,
the beam moves 30° toward the left, that is, in the backfire direction.

‘See Sec. 11-3.

Sec. 913]

THE AN/APQ -7 (EAGLE) SCANNER

293

If the waveguide carries the energy from right to left, the scan extends
for 30° to the right of the center line of the aircraft. By feeding r-f power
into the ends of the array alternately, a total scan of 60° is realized.
This alternate-end technique is always used in practice with the Eagle
scanner; it is accomplished with the aid of a fast-acting r-f switch which
operates synchronously with the guide-squeezing mechanism.

The azimuth beam angle 6 is related to the guide width a, the dipole
spacing s and the free-space wavelength X 0 by the formula

Here 6 is positive in the end-fire direction.

No provision is made for tilting the beam in elevation. Fixed 16-ft
aluminum flaps (Fig. 9T9) above and below the array serve to shape the
beam in elevation to a roughly cosecant-squared distribution.

Fig. 9-20.—Back view of part of AN/APQ-7 scanner, showing toggles.

The fixed aluminum channel, which measures about 2f in. by 5f in.
by 16 ft over all, is first extruded, after which the critical surfaces are
machined. The plate is similarly manufactured. The plate is linked
to the channel by a system of 10 pairs of toggles and a tie rod, as shown
in Fig. 9-20. A cam actuates the motion of the plate, while the linkage
holds the a dimension uniform along the variable waveguide. To one
of the toggles is attached a cam so cut as to drive a synchro data take-off
through an angle equal to 6.

The chokes shown in the channel and in the plate serve to prevent
leakage from the varying guide so that the loss due both to the finite
conductivity of the waveguide and to the leakage past the long choke
is kept down to about -j db/m during most of the scan. Although the
wavelength in the guide is nearly that which would be indicated by the a
dimension, small corrections must be allowed for the chokes and for any
variation of the clearance between the channel and the plate at the
chokes. For this reason the b dimension is maintained to a close tolerance
by means of rollers constraining the movable plate (Fig. 9-21). It has
been found very profitable to adjust variations in the effective guide

294 ANTENNAS, SCANNERS, AND STABILIZATION [Sec. 913

width (or the phasing) by means of screw adjustments on the toggles of
the squeeze mechanism. The a dimension is adjusted within a few

Fig. 9-21.—End view of AN/APQ-7 scanner.

thousandths of an inch as measured by an inside micrometer, after which
the antenna is set up and its gain maximized by adjustment of the toggle

j All the dipoles shown in Figs.

9-19 an d 9-22 are horizontal and
1 therefore radiate energy polarized

horizontally; but alternate dipoles are
O' 351 ’ | | reversed end-for-end in assembling

I i-’J T the array. The spacing between

n II | i 1* m

I j | the centers of adjacent dipoles is

II l I 16 0.315' one-half the guide wavelength when

~~^ the guide is 1.200 in. wide. There-

^fore in each adjacent pair the dipoles
i i are excited in phase opposition; but

j j because of the reversal of one of them

i | I 0.143'id they radiate in phase, producing a

broadside beam. If alternate di-

Fig. 9-22.—Construction of dipoles used poles were absent the beam would
m an/apq- 7 antenna. still be formed, but would be ac¬

companied by other strong beams comparable to undesired orders of dif¬
fraction from an optical diffraction grating. As it is, the side lobes are
from 2 to 5 per cent as intense as the main beam.

296

ANTENNAS, SCANNERS, AND STABILIZATION [Sec. 914

to be described was developed for the 3-cm band to provide coastal
defense batteries with accurate target position and “splash-spotting”
data for fire control. An azimuth beamwidth of 0.55° and a short pulse
(t Msec) make accurate tracking possible in both azimuth and range.
The sector that is rapidly scanned is 10° wide and the center of this sector
may be swung to any azimuth position for search purposes.

Externally the scanner consists of a mount, which ordinarily rests on a
tower platform; the antenna housing, 143 by 56 by 27.5 in., constructed

of plywood; and the copper-coated plywood reflector, 2 by 12 ft, hinged
to the deck of the housing (Fig. 9-25). The reflector is a half parabolic
cylinder of 1-ft focal length, and is fed by the 11-ft by 1.4-in. linear
aperture of the enclosed portion of the antenna to produce the beam 0.55°
in azimuth by 3° in elevation. Terminating in this aperture is a long
“horn,” a parallel-plate region of copper-coated plywood, folded as in Fig.
9-26. The conducting surfaces are spaced % in. apart and increase in
width from about 2 ft at the edge A A to about 11 ft at the edge BB.
This horn extends over a length of about 12 ft and is folded three times.
The feeding edge AA of the parallel plates consists of a boundary which
forms a 90° arc, 14£ in. in radius. Radiation is fed into the parallel
plates between these flanges by four feed horns, each 2 in. wide, with
suitable chokes meeting the flanges. The four horns are mounted on
four radial waveguides which are fed at their intersection by a four-way
r-f sector switch (Fig. 9 27). This switch consists mainly of a rotary
joint 1 which terminates in four waveguides F at 90° to each other. These

‘See Fig. 1113.

Sec. 914]

SCHWARZSCHILD ANTENNA

297

arms rotate at 240 rpm, as do the four arms H which support the feed
horns. They remain in the angular relation shown. Between the two
sets of arms is a stationary ring with a 105° window through which
energy may pass into whichever feed horn is opposite the feeding edge
of the folded horn. When the horns and switch are rotated the effect
is to cause the beam of the antenna to scan a 10° azimuth sector each

Fig. 9-25.—Perspective of horn, reflector, and feed of Schwarzschild antenna used in

AN/MPG-1.

time a horn runs its 90° course. Since about 10° of the 90° are lost in
switching, we can think of the parallel-plate region as effecting an 8-to-l
optical reduction from the 80° scan of the broad-beamed primary horn
to the 10° scan of the very sharp antenna beam.

The transformation of the moving feed horn into the scanning beam
is made by means of two double-curved bends CC and DD in the parallel
plates (Fig. 9-26). Although one parabolic bend CC would serve to
collimate the primary radiation and provide a sharp beam on axis, two
bends may be so designed as to correct for coma and thus give a good
beam off axis as well. The theory of two-mirror telescopes was used to
calculate the bends for the Schwarzschild antenna. The cylindrical

298

ANTENNAS, SCANNERS, AND STABILIZATION [Sec. 915

bend EE near the aperture has no optical effect and was introduced for
the sake of compactness. A plastic closure prevents moisture from
entering the horn at the edge BB. Accurate wood-working makes possi¬
ble the use of plywood construction which is preferable to aluminum in
weight and ease of manufacture.

The drive motor runs at 1725 rpm and is connected by a 7-to-l gear
reduction to run the rotor about 4 rps. The azimuth data transmitter
is a capacitive voltage divider connected to a high-frequency oscillator.

Fio. 9-26.—Successive steps imagined in folding the Schwarzschild horn.

The voltage developed across one of the condensers is detected and
applied to the indicator. This condenser is of the variable rotary type
and is driven at 16 rps, i.e., one revolution per scan.

The antenna is mounted on the vertical axis of the mount used for
the SCR-584 antenna, with certain alterations.

Approximately 100 plywood antennas were constructed during the
war. The production models that saw service showed no deterioration
over a period of one year.

9T5. SCI Height Finder .—This antenna is intended for use in rapid
coverage height-finding. 1 It is one of a pair of antennas (Fig. 9-28)
mounted on the same pedestal and rotating together in azimuth at 4
rpm. The other antenna is used for long-range search and azimuth

1 C. V. Robinson, “The SCI Rapid Scan Height-finding Antenna,” RL Report
No. 688

Sec. 9-15]

SCI HEIGHT FINDER

299

determination. The height-finder beam, at the 10-cm band, is 3.5° in
azimuth by 1.2° in elevation, and scans linearly one way for 10.5° in
elevation from the horizon up, ten times a second. It makes continuous
height-finding possible on small aircraft out to 50 miles, and farther on
larger planes.

The principal elements of the antenna are a 5- by 15-ft grating reflec¬
tor which stands on end, an 8- by 2- by 1-ft convoluted parallel-plate
horn whose aperture is 5 ft from the reflector, and a rotating waveguide
feeding the horn. The feed, which does not show in Fig. 9-28, is driven
by a motor in the box attached to the horn. The parallel-plate horn
serves to transform the circularly moving waveguide feed into an appar¬
ently linearly moving source. The beam scans 10.5° in elevation for
each rotation of the guide.

The principle may be better understood by considering a simplified
antenna which consists of a reflector and parallel trapezoidal plates with a
long flared base “illuminating” the reflector; the plates are fed with

Height-finder reflector 5 ft by 15 ft
t#oo for electronic equipment ^

Robinson etectrfcaMy^
scanning feed

Line source and plastic
closure N

Fio. 9-28.—The three-aris antenna mount of the SCI radar,
principle is the same as moving the feed in an ordinary paraboloid reflec¬
tor. The reflector for this antenna is not paraboloidal* however, but is
astigmatic, having different focal lengths in the horizontal and vertical
planes because the points of divergence of the rays in the feed differ in
the two planes.

300 ANTENNAS, SCANNERS, AND STABILIZATION [Sec. 915

perpendicularly polarized waves by a waveguide at the small base (Fig.
9-29). As the waveguide feed horn is moved from top to bottom, the
beavertail beam scans from minimum elevation angle to maximum. The

Azimuth search
reflector

Sec. 915]

SCI HEIGHT FINDER

301

In actual fact, the feed horn moves, not linearly, but circularly. The
rotating feature is achieved by folding and bending the trapezoidal plates,
keeping them parallel with a minimum of stretching, in such a way that
the feed base is rolled into a complete annular aperture while the flared
base is held straight. Figure 9 30 illustrates how this can be done with a
single trapezoidal sheet. Various additional mechanical and electrical
complications appear when a two-sheet metal horn is made in this shape,
but the convoluted parallel-plate region has substantially the same optical

9-29.—Simplified SCI height finder, side view.

properties as the trapezoidal plates before rolling. When the rotating
guide feeds into the annular aperture of the horn, the beam describes a
linear “fro” scan in elevation. The feed position marked O in Fig. 9-30
gives a beam on axis. When the feed is in the neighborhood of the cross¬
over point (about £ of the time required for one complete scan) the signal
is ambiguous because there are two beams.

The parallel-plate assembly consists of two fabricated aluminum
surfaces spaced f in. apart, each consisting of a cast and machined center
portion which supports a ribbed sheet metal “wing” section above and
below. Specially designed steel posts are used to help maintain the
spacing between these surfaces without ill effect on the electric waves.
The rotary waveguide feed was made radial for compactness, resulting in
the arrangement of the horn, chokes, and annular aperture shown in
Fig. 9-31. The absorbing septum shown in this figure was introduced to
reduce the amount of ambiguity caused by a double beam and to improve

302

ANTENNAS, SCANNERS, AND STABILIZATION ISec. 9 16

the impedance match in this angular region by absorbing such radiation
as may try to leak across that region as the horn approaches.

9T6. Other Types of Electrical Scanners. —Probably the first electri¬
cal scanner to be used, developed by Bell Telephone Laboratories, operates

This triangular

Fig. 9-30.— Illustration of trapezoid before, during, and after rolling.

Fig. 9-31.— Detail of radial feed horn.

Sec. 916]

OTHER TYPES OF ELECTRICAL SCANNERS

303

at about 10 cm and produces a beam 2° in azimuth by 6.5° in elevation,
which scans 29° one way in azimuth 10 times per second. The antenna
radiates by means of an array of 3 by 14 polyrod radiators (Fig. 9-32).
Each of the 14 vertical rows of 3 elements is phased as a unit and the

Fig. 9 32.— Array of end-fire polyrod radiators.

units are phased linearly by a row of rotary phase shifters, each of which
adds 720° of phase per revolution.

An interesting array-type antenna which reached a highly developed
experimental stage is the Long Range, Aircraft to Surface Vessel, LRASV,
corrugated coaxial line array. This antenna was designed to be used
with a 10-cm system, mounted as a long array feeding a reflector along
the side of an airplane, giving a beam 0.8° by 9° for long-range search.
The array, shown in Fig. 9 33, consists of a 15-ft coaxial line whose outer
conductor is pierced with radiating slots spaced at intervals of 2i in.,
which is less than the wavelength. The inner conductor consists of a
i-in. shaft on which are many r^-in. diameter eccentric disks which serve

304

ANTENNAS, SCANNERS, AND STABILIZATION [Sec. 9 16

to make the wavelength less in the line than in free space. This shaft is
displaced from the axis of the outer conductor and supported by bearings
at 10-in. intervals so that it can rotate. As the inner conductor turns,
the wavelength in the line varies, causing the beam to scan 6.5°. Larger
scans by this method are quite feasible.

Another rolled parallel-plate scanning antenna, similar to the type
described in Sec. 9T5 in the respect of having a single rotary waveguide
feed, and also capable of rapid scan, has been developed. The equiva-

Wave fronts

(a) ( b )

Fig. 9-34.—Reflector roll scanner.

lent simple antenna is a polystyrene lens placed between parallel trape¬
zoidal conducting plates and fed by a waveguide at one edge of the plates
(Fig. 9-34a). Moving the guide tilts the beam. A conducting reflector
strip is placed between the plates in such a way that the waveguide feeds
the lens from an adjacent edge of the plates (Fig. 9-34b). It is now
possible to roll up plates and reflector strip in such a way that the feed
path is annular. This type of roll is ordinarily simpler to build than the
one described in Sec. 9T5.

In general it can be said that antennas of the array type (Eagle and
LRASV) are compact but that the beam position depends on the fre¬
quency, while antennas of the parallel-plate type (for instance, Schwarz-
schild, SCI) have a beam position independent of frequency but have
more bulk and weight. Thus, the array has found use in airborne work
and mobile equipment, while the others tend to be used in ground and
ship equipments.

THE STABILIZATION PROBLEM

Airplanes and ocean vessels are unsteady bases from which to make
observations by radar or by any other means. It has been necessary to

Sec. 9-17]

STABILIZATION OF THE BEAM

305

devise means of compensating for the angular motions of such vehicles,
and this practice is known as stabilization. 1 The technique falls into
two broad divisions, depending on whether the beam of radiation is
stabilized, or the data displayed on the indicator are stabilized or cor¬
rected for the distortions caused by a tilting vehicle.

In general there is no choice between the two types of stabilization.
If the vehicle rolls or pitches to such an extent that its search radar no
longer scans the desired part of the field of view, beam stabilization is
necessary. This will prevent targets from fading from the indicator; if
they are then indicated, but at a false position, data stabilization becomes
a concurrent need. If the vehicle momentarily changes heading (yaws)
while on a certain course, the relative azimuth of targets will momentarily
alter; the consequent aberration of the display can be, and has been, cor¬
rected by either type of stabilization. Either sort of stabilization
requires the vehicle to carry gyroscopes or other devices which are sensi¬
tive to direction in space and “know” the direction of north or up.

There are several ways of more or less completely mechanizing the
stabilization of the beam. The most obvious and perhaps the most
elegant is to provide a stable base for the scanner. This may be a plat¬
form mounted on gimbals and controlled automatically to compensate
the pitching and rolling of the vehicle. If the vehicle rolls much but
pitches little, the pitch-gimbal axis may be omitted, and the stable-base
stabilization degenerates into roll stabilization.

A very different method of beam stabilization is possible in a scanner
having its main axis always perpendicular to the floor of the vehicle.
Use is made of the tilt axis of the antenna to the end that the antenna is
automatically directed toward the horizon, or to whatever angle above or
below the horizon is desired. The line of sight is thereby stabilized.

9T7. Stabilization of the Beam. Airborne Antenna Stabilization . 2 —
Antenna stabilization for airborne radar is a scheme to preserve the same
conditions of radiation illumination in nonlevel flight as in level flight.
This is necessary to prevent (1) uneven illumination of the area being
scanned, (2) loss of radar range, or (3) distortion of the PPI presentation.
Stabilization equipment must be designed and constructed to stabilize
the beam of radiation, whether it be pencil or fan, against any maneuver
of the aircraft such as a climb, a glide, or any combination thereof. This
must be accomplished with components that are not affected by the
various accelerations, attitudes, or vibrations which might be encoun¬
tered in turns, climbs, glides, or banks.

A stabilizer may generally be broken down into three main com¬
ponents: the gyroscope with its potentiometer or synchro take-offs, the

1 The theory and methods of stabilization are discussed in Vol. 26 of this series.

2 By F. B. Lincoln.

306

ANTENNAS, SCANNERS, AND STABILIZATION [Sec. 9-17

servoamplifier, and the follow-up system which includes the servomotor,
the gear train or linkage system, and a take-off actuated by the con¬
trolled member. The gyro may be mounted on the rotating scanner or
remote from the scanner, using slip rings and resolvers to take off the
required error information. The error is fed into a servoamplifier whose
output operates the servomotor which in turn aligns the antenna with
the horizontal through a gear train or linkage system.

The gyro should preferably have either a two-speed erection mecha¬
nism or a device to disconnect the erection mechanism when the aircraft
goes into a turn. In a turn the gyro rotor tends to align itself with the
resultant of the true gravity and the centrifugal force caused by the
acceleration in the turn, instead of with true gravity alone. This can be
minimized or eliminated by using a two-speed erection mechanism, or by
employing an electromagnetic clutch to throw out the erection system
entirely in turns.

Continuing the general classification previously referred to, stabilizers
may be further typed as stable-base, roll, or line-of-sight, depending on
the stabilization compensation afforded.

The stable-base stabilizer, as the name indicates, provides complete
stabilization of the platform upon which the antenna is mounted. This
requires use of a two-axis gyro transmitter to provide alignment or error
information for both roll and pitch axes. The gyro is usually mounted
remotely from the antenna structure in this type. In addition two
separate servoamplifiers and follow-up channels are required, one for the
roll-error component and one for the pitch-error component. Although
this provides complete stabilization, the weight of the components usually
appears excessive so that another type is preferable.

The roll stabilization referred to is stable-base stabilization with the
pitch channel removed. This requires a single-axis gyro transmitter for
the roll axis, and but one servoamplifier and follow-up channel. Roll
stabilization would be appropriate in large aircraft for which the pitch
component might be negligible or tolerable. In deciding between a roll
and a platform stabilizer the accuracy requirements must be balanced
against the weight added by the pitch channel.

The line-of-sight method is one which maintains the axis of the beam
of radiation in a horizontal position or a fixed angular distance above or
below the horizon as the antenna rotates, scanning the horizon. This is
done by automatically tilting the antenna about an axis perpendicular to
the plane of the beam and parallel to the floor of the aircraft. Figure 9-35
shows the stabilizing attachment, AX/APA-15, mounted for photographic
test on the scanner of the AX/APS-2 circular-scanning radar. The black
tubular construction of the scanner yoke can be seen, together with the
silver-plated £-in. coaxial transmission line. The 29-in. paraboloid has

Sec. 9-17]

STABILIZATION OF THE BEAM

307

been removed from the gently curved support casting, which can be seen
supported between the tilt bearings at the tips of the yoke. A table
clamped to the yoke supports the gyro-torque unit and a servoamplifier.
The gyro is mounted in gimbals and is provided with one synchro take-off

Fig. 9-35.—A stabilizing attachment mounted on an airborne scanner. The reflector has
been replaced by a camera for test purposes.

at the gimbal axis parallel to the tilt axis. A synchro is also located at
the output crankshaft of the torque unit. The servoamplifier essentially
amplifies the algebraic difference between the voltages from these take¬
offs, and thus actuates the motor in the torque unit to assure alignment
between the output shaft and the gyro. The output shaft is linked to the
paraboloid support by a rod seen at the bottom of Fig. 9-35. When there

308

ANTENNAS, SCANNERS, AND STABILIZATION [Sec. 917

is a misalignment between the beam axis and horizontal, the synchros in
the gyro-torque unit transmit the error to the amplifier, a phase-sensitive
detector whose output controls the servomotor, which in turn causes the
linkage system to tilt the antenna up or down until the beam axis is again
horizontal. Because the gyro is mounted on the scanner, it is liable to
the precession caused by the inertia of the supporting gimbal system.
Under some conditions this precession causes the gyro to indicate a false
vertical, thus producing serious errors in the stabilization system.

Although in the above example the gyro is mounted on the rotating
yoke, the effects of precession are avoided in the most recent designs
by mounting the gyro on the airframe and providing a take-off on each
gimbal axis. A voltage indicating the correct tilt angle is fed to the
servoamplifier. A special rotary inductor mounted on the scanner base
provides this voltage, which it computes as a function of the antenna
relative azimuth and the roll and pitch voltages from the gyro.

As previously discussed, the purpose of antenna stabilization is to
preserve range performance by assuring constant illumination in non¬
level flight as in level flight. In considering the accuracy requirements
various factors must be compared, such as beam shape and operational
use contemplated for the radar. If a pencil beam moves up or down
because of maneuvers of the aircraft or poor stabilization, the scope
signal will fade. Quantitatively, if a beam moves up or down by one-half
its beamwidth, it can be shown that the set will suffer a range reduction
of 29 per cent. The range will be reduced 10 per cent if the beam varies
from the stabilized position by 0.28 beamwidth and by 5 per cent if the
beam varies 0.19 beamwidth. As a range reduction of 10 per cent is
considered the maximum allowable, it can be seen that the beam must be
stabilized so that it remains within 0.28 beamwidth of a completely
stabilized position. The adequacy of the above calculations has been
verified by rough observations in flight. Beam stabilization in current
airborne navigation radars should be accurate within about ± 1.3°,
depending on the set, lest range performance suffer noticeably.

In practice it is quite difficult to realize stabilization accuracies high
enough to satisfy the foregoing tolerances for the various types of beams
and radars. This is principally due to the early stage of airborne stabili¬
zation development and the stringent weight requirements on airborne
gyroscopes. Current developments should lead to more highly accurate
lightweight airborne antenna stabilization. The present static accuracy
of airborne gyros ranges from ± to + However, errors of from
1° to 5° may occur if the erection mechanism is not cut off in a turn.
This error is a function of the duration of the turn.

Shipborne Antenna Stabilization .—In recent practice the stabilization
of airborne ground-mapping antennas is by the line-of-sight method, in

Sec. 917]

STABILIZATION OF THE BEAM

309

V/ \

\ \

.Deck plane

Horizon

plane

which the scanner has two degrees of freedom, corresponding to the train
(azimuth) and elevation axes. In shipborne radar it has become evident
that for certain applications a third axis should be added to ensure a true
and undistorted display of the radar signals. The nature of these dis¬
tortions will be clear from the following considerations. When a ship
and its two-axis antenna mount are rolled to the right and the elevation
axis momentarily set athwartship
so that the antenna is looking for¬
ward, if the elevation angle of the
beam is varied the beam thereupon
describes on the sky the arc of a
great circle which is not vertical
but which is inclined toward the
right. All airplanes detected on
this arc wall be indicated as dead
ahead, since the train axis is ori¬
ented to this position. This indi¬
cation is of course false, and the
two-axis mount therefore imper¬
fect in principle.

The computer described below
provides correction for distortion
of this type. Such correction is,
however, inapplicable if the radiation is a vertically fanned beam or a
pencil beam which must oscillate rapidly in a vertical plane.

The inadequacy of two-axis ship antenna mounts for certain applica¬
tions can be corrected by the addition of a third degree of freedom, cor¬
responding to the cross-level axis. This axis is supported by the train
axis and is set parallel to the deck; the elevation axis is mounted on it at a
right angle. By means of this new degree of freedom a servomechanism
holds the elevation axis level in respect to the horizon. The axes of this
three-axis mount are commonly designated as the “train,” “cross-level,”
and “level” axes. A mount of this type affords freedom from the dis¬
tortion of the display occurring when a two-axis mount is used. It has
the added virtue that it can follow moving targets above 45°, which with
a two-axis mount would require impracticably great servo rates. Weight
considerations have prevented the development of three-axis scanners
for airborne use.

We have mentioned a distortion in the display of an elevated target
observed from a rocking ship. A closely related distortion in bearing is
present even for surface targets: the deck-tilt error. Its origin is made
clear by an example, Fig. 9-36, which represents a ship heading north
toward the reader, listing to starboard. The circle represents a large

Fig. 9-36.—Deck-tilt error. The arc HB,
which is the bearing of the beam, is greater
than the arc HA, which is the bearing as in¬
dicated if deck-tilt error is not compensated
MBA represents a meridian on a sphere.

310

ANTENNAS, SCANNERS, AND STABILIZATION [Sec. 9-17

sphere with the antenna imagined at its center. All lettered points are
on the sphere: Z is the zenith, M is the prolongation of the mast, and H
is the ship’s heading. If the antenna is not stabilized, its pencil beam will
at some instant be directed toward A below the horizon. The indicator
will then show an angle measured by the arc HA. If the beam is stabi¬
lized by a two-axis mount, it will at that instant be at the point B where
the great circle AM intersects the horizon; since HB exceeds HA the
indicator will report the position of the beam falsely. If the beam is
stabilized by a three-axis mount, it will be directed toward C; the indica¬
tion is again false since HC is less than HA. Thus either of these types
of stabilization results in a distortion of the bearing of targets on the
horizon.

A recent successful device for the stabilization of shipborne antennas
includes computers and an associated gyroscope, and is located wi, hin the
ship. The principal components of the stable vertical gyroscope are a
gimbal system so supported that the outer and inner gimbal rings tilt
respectively about the roll and pitch axes of the ship, a second gimbal
system supported by and within the first, and the gyroscope wheel sup¬
ported in the second gimbal system. The wheel axis seeks the vertical
because of a pendulous magnet carried by a third gimbal system, and
compensation is provided in the gyroscope for the effect of ship’s turns or
changes of speed.

The second gimbal system is held parallel to the plane of the gyro
wheel, that is, horizontal, by means of a servomechanism; and from this
gimbal system two push-rods extend upward and provide roll and pitch
inputs to the mechanical computer located immediately over the gyro
unit. The force to move these rods is provided by the servomechanism
rather than by the gyro itself. In addition to roll and pitch, the desired
angular position of the beam in space is fed to the co.'-puter as another
mechanical input provided by a servomechanism. The cc nputer is
kinematically equivalent to a small replica of the antenna mount which
is to be stabilized. The outputs are the deck-tilt correction and elevation
angle for a two-axis mount, or deck-tilt correction and level and cross¬
level angles for a three-axis mount. They are mechanical but are converted
to voltages by means of synchros, and control the servomechanisms
which actuate the motors for the three axes of the mount.

More than one computer located on the gyro unit can be actuated
simultaneously, making possible the simultaneous stabilization of more
than one antenna. No computer is needed in stabilizing stable-base
mounts, since roll and pitch data are furnished directly from the stable
vertical.

Returning for the moment to generalities, two alternative methods
are at hand by which the deck-tilt, correction can be effected. One is to

Sec. 9-18]

DATA STABILIZATION

311

let the antenna scan uniformly during search and to control the deflecting
coil of the indicator to correct the deck-tilt error. This is a species of
data stabilization; it is not commonly used. The other cure for the
deck-tilt error is to drive the azimuth sweep of the radar indicator at a
constant rate during search and to control the train angle of the antenna
by means of a computer and servomechanism. As we have seen, it is one
of the functions of the computer to provide the deck-tilt correction.
This computation is easily mechanized, because the deck-tilt error is
mathematically similar to the error in transmitting angular motion
through a universal joint.

The gyroscopes used in shipbome antenna stabilization are accurate
to within 2' to 7'; the error seems to be a function of the roll, pitch, and
heading of the vessel. The large synchros used in this W'ork are liable
to err by about 10' to 30'. It follows that a good shipbome equipment,
using synchros geared as high as 36 to 1 for increased accuracy, holds the
beam with an average error of as little as 5', although momentary errors
of more than twice this magnitude may arise.

9-18. Data Stabilization. 1 —It has been remarked that even after the
mechanical engineer has provided a stabilized antenna mount and thereby
ensured that the radar will correctly perform its scanning function despite
rolling or pitching of the vehicle, the indicator may still display the posi¬
tion of targets falsely. We are concerned in this section with the problem
of improving the indicator in this respect.

The older PPI radars, both airborne and shipbome, were designed to
display targets at their bearings relative to the heading of the vehicle.
More recent design allows a display of targets in their true bearings, that
is, with north at the top of the screen regardless of heading. The rela¬
tive-bearing indication is bad for two reasons: (1) the entire display
rotates and becomes confused if the course of the vehicle is altered; (2)
the natural random changes in the heading of the vehicle cause a cor¬
responding blurring of the display on the persistent screen. The true-
bearing indication is free of these faults. It is a data stabilization in
regard to yaw and changes of heading.

Yaw stabilization is implemented with the aid of a horizontal gyro¬
scope which is kept pointing north by manual or automatic reference to
the earth’s magnetic field. Through a mechanical or electrical differen¬
tial there is provided at the indicator a voltage signifying the true bearing
of the beam, that is, the difference between the relative bearing of the
beam and the relative bearing of the true north.

Deck-tilt error is serious in airborne as w T ell as in shipbome radar.
Let us imagine an airplane equipped with a bombing radar having a fan
beam; the base of the scanner is not stabilized, and the antenna may or

1 Secs. 918-9-20 by W. M. Cady.

312

ANTENNAS, SCANNERS, AND STABILIZATION [Sec. 919

may not be line-of-sight stabilized. If this airplane banks, the relative
bearing of ground targets will be, as we shall see, falsely indicated. For
example, let us consider the case of an airplane banking for a right turn,
the relative bearing of the beam being straight ahead. It is clear that
since the fan is perpendicular to the floor of the airplane it is not at the
moment vertical, and that therefore the targets on the straight line on
the ground now being illuminated by the beam are not at zero bearing.
Since such targets are nevertheless displayed as if at zero bearing, the
display is distorted; these targets are shifted by an amount equal to the
altitude of the airplane multiplied by the tangent of the bank angle.
Other targets are less seriously disturbed, those at 90° and 270° being
correctly indicated on a banking airplane.

Two methods have been considered for correcting the airborne deck-
tilt error. One method is so to stabilize the antenna that the plane of the
fan beam remains indeed vertical. This can be accomplished by stable-
base stabilization or by a three-axis mount. The other method is by
data stabilization, and several circuits have been devised for removing
the distortion if supplied with voltages depending on the angles involved.
None of these circuits has been incorporated in systems now in wide use,
although one radar designed for production incorporates a feature that
accurately corrects the display at the one target designated as the aiming
point.

9T9. Installation of Airborne Scanners.—In discussing antenna
installations we will treat first the airborne case. Here, one of the press¬
ing problems is the choice of location. The radar must have the unob¬
structed “vision” required for its operation, and its antenna should be so
installed that it may be housed in an aerodynamically acceptable radome.

A very common requirement is circular vision of the ground well out
toward the horizon, as in Fig. 9-6. The only good location is then below
the fuselage. If rearward vision is not required, an antenna with circular
scan can be mounted just behind and below the nose of the airplane, where
the radome can be completely faired in.

Scanning of only a forward sector is possible if the antenna is mounted
in the nose. Such a location is impossible in single-engine airplanes, and
external housing becomes necessary. Aerodynamically, perhaps the
best site in this category is at a wing tip, although a blister faired into a
leading edge has been widely used. For maintenance reasons easy
replacement of the set is desirable; this has been accomplished in one
instance by packaging the greater part of the set in a “bomb” suspended
under one wing. In the aircraft-interception radar of nightfighters the
scanner is located for vision in all generally forward directions. Such
scanners can be mounted in any of the locations that are good for sector
scanners. Bomber-borne scanners for protective fire control are located

Sec. 9-20] INSTALLATION OF SURFACE-BASED SCANNERS

313

where they can search for and track enemy fighters approaching from the
rear or other anticipated directions, or are located on the turret guns.

An important question in mounting a scanner in the belly of an air¬
plane is “ How far shall the antenna protrude below the keel line?” Too
great a protrusion will add to the aerodynamic drag, whereas if the
antenna is retracted too far the vision is inadequate in nearly horizontal
directions because of partial blocking of the field of radiation. The ray
diagram of the radiation field is not a sufficient guide in planning an
antenna installation. In prototyping each installation the minimum
protrusion allowable from the standpoint of the diffraction of the radia¬
tion must be determined by measurements of the antenna pattern made

Fig. 9-37. —The ray diagram shows that fan-beam antenna may be installed partly inside

the fuselage.

with the antenna installed in a mockup. 1 Such measurements have
shown that some circularly scanning fan-beam antennas may be so
installed that nearly half their height is above the keel line of the airplane,
and this conclusion has been confirmed in observation of the indicator in
flight. Figure 9 37 shows qualitatively why such an installation is possi¬
ble with the type of scanner shown in Fig. 9-8.

In attaching the scanner to the airframe it is not necessary or advisable
to use shock mounts unless electronic equipment is inseparably attached
to the scanner. It is frequently essential, however, to provide adjust¬
ments for accurately orienting the scanner base. To allow this adjust¬
ment it is customary that the short length of transmission line between
the scanner and the r-f unit be flexible: this flexibility also allows the r-f
unit to be shock-mounted.

9-20. Installation of Surface-based Scanners.—The installation of
scanners on shipboard presents a siting problem slightly simpler than in
the airborne case. It is necessary to avoid locations where the structure
of the ship will blank the radiation or produce spurious reflections.
Sometimes it becomes necessary to install two scanners, each of which
covers the region in which the other is blind. When a ship has more than
one radar on a given wavelength, one can “jam” the other, filling its
screen with spurious indications; this effect can be mitigated by proper
siting of the scanners and by blanking the receiver of each at the instant

1 A recent installation is described by W. M. Cady in RL Report No. 848, “The
AN/APQ-13 (60-in.) Scanner in B-29 Airplanes.” See also Figs. 9-7, 9-8, and 9-39.

314

ANTENNAS, SCANNERS, AND STABILIZATION [Sec. 9-21

the other is transmitting a pulse. On account of the curvature of the
earth and for reasons of microwave propagation it is usually advantageous
that the scanner be installed as high as possible. Radomes are not widely
used to house shipboard scanners, the tendency being to make the
antennas of such low wind resistance and such sturdy construction as to
render radomes unnecessary.

Ground-based radars may be grouped, according to their mobility,
as transportable, mobile, and fixed. Because the transportable scanners
are disassembled for moving, their installation requirements include
easy assembly. The AN/TPS-10 scanner shown in Fig. 9T5 disassem¬
bles into small parts for easy mobility in mountainous terrain. A firm
and adjustable footing must be incorporated for transportable scanners.
A truck or trailer on which a scanner is mounted must also be firmly
braced while the radar is in use; the scanner itself must be adjustably
mounted to the vehicle, if accurate position-finding is desired.

The siting of ground-based scanners is to be regarded as an aspect of
the installation problem. A suitable site must be one where no mountain
seriously blocks off the region beyond. A more subtle siting requirement
is the avoidance of ground “clutter”; permanent echoes are bothersome
at certain sites, particularly if the radar targets frequently pass at nearly
the same range and direction as such echoes. Moving-target indication,
discussed in Chap. 16, is now practicable to alleviate ground clutter.

9-21. Radomes. 1 —It is necessary to protect all airborne and some
surface-based microwave antennas from wind and weather. The pro¬
tective housings have come to be known as “radomes.” A fuller discus¬
sion than the following will be found in Vol. 26 of this series.

The circular cylinder shape was early used for the radome. For such
a shape the radiation falls on the radome essentially at normal incidence,
the angle of incidence being defined as the angle between the incident
radiation and the normal to the surface at the point of incidence.

The development of microwave airborne radar systems forced the
development of the science and art of radome design. It resulted in
amplification of the electrical theory for radomes through which the radar
beam passes at high angles of incidence. Plywood, first used for radome
construction, gave way to more satisfactory synthetic materials; and
aerodynamics, at first ignored, was given consideration in the design.
Excellent installations are possible if the radar systems are considered in
the initial design studies of aircraft.

Since the airborne radome involves all the problems of the surface-
based installation in addition to many others peculiar to itself, this
discussion will be limited to the airborne case. Some of the factors con¬
trolling the design of an airborne radome are the radar antenna and its

1 Secs 9-21-9-25 by F. J. Mehringer.

Sec. 9 22]

STREAMLINING

315

function, radome materials, transmission of radar energy, structural
requirements, aerodynamics, access to the radome cavity, and specifica¬
tion and test.

In this discussion only the three major items—aerodynamics, elec¬
trical transmission, and structural design—will be discussed, and these
only briefly. None of these items can take preeminence over the others
since a design aerodynamieally or structurally poor can prevent the radar
set from being useful, just as would a radome that had faulty transmission
characteristics. The radome design must, therefore, be a compromise
of these three major factors if accuracy and effectiveness of the airborne
unit are to be secured.

9-22. Streamlining.—There is no simple foolproof answer to the
aerodynamical problem. Each installation has peculiarities of its own,
depending upon its location on the airplane in question, the plane itself,
the speed of the plane, and the size and shape of the radome. A few
simple considerations can be set forth but the real answer can only result
from careful test in a wind tunnel.

Although, from an electrical viewpoint, the circular cylinder is the
most desirable shape for a radome, aerodynamieally it is objectionable
due to its high drag. By streamlining a cylinder its air resistance can be
reduced to a sixth or less. Any radome extending beyond the fuselage
line of the airplane should therefore be streamlined.

The drag for a protuberance of given shape increases in approximate
proportion to its frontal area. It is therefore desirable to reduce the
projected area of the radome as much as possible even to the extent of
having the radome surface coincide with the skin of the plane.

If a protuberance is necessary, the drag can be minimized by locating
the radome at a position where there is already some disturbance of the
airflow. The turbulence of the air stream tends to be a maximum toward
the tail of the plane. While practically no protuberance is permissible
near the nose of a high-speed airplane, one extending several inches amid-
ship or further aft may cause a hardly noticeable increase of drag.

The truly satisfactory design, however, can be verified only by tests
in the wind tunnel where very slight differences in aircraft performance
are readily detectable. The wind-tunnel test can also be used to furnish
pressure distributions on the radome surface, which are necessary for the
structural design computations.

The location of the antenna on the airplane must also be the result of
operational requirements and compromises with the other components.
For navigation and bombing it is desirable to have the antenna scan 360°
in azimuth. This can best be realized in a location on the belly of the
plane about midship, but generally only by adding a large protuberance.
A location in the “chin” of the airplane offers a more favorable location

31G

ANTENNAS, SCANNERS, AND STABILIZATION [Sec. 9-23

so far as the aerodynamics is concerned, but limits the rearward view.
This space, too, is desirable for the location of certain crew members and
of the bombsight. Interference with other installations is usually less in
an aft location, but the space is often limited by the size of the fuselage
at this point and the forward view may be cut off by the forward portion
of the plane.

9-23. Electrical Transmission. —The ultimate shape of the radome is
generally limited by electrical design considerations. The retraction of
the antenna is controlled by edge interference, for an edge can cause
blanking and diffraction of a radar beam. The result is a distortion and
deterioration of the antenna pattern. Any discontinuity such as that
caused by reinforcement of the radome or by a piece of metal may cause
diffraction if it intercepts the radar beam.

The permissible range of incident angle is the other electrical factor
limiting the shape of the radome. The range of satisfactory incident
radiation transmission varies with different materials and radome wall
constructions. The properties of the materials affecting the transmission
are the dielectric constant and the loss tangent; the latter is an index of
the absorption and the former is a factor determining the reflection. For
optimum combinations to date, satisfactory transmission can be obtained
over a range of 0° to 70°. Beyond this value the transmission decreases
very rapidly, reaching zero transmission at 90° incidence.

Having determined a reasonable shape for the radome, it is then neces¬
sary to check the angles of incidence by means of an antenna ray diagram.
Typical ray diagrams for cosecant-squared antennas are shown in Figs.
9-2, 9T0, and 9-37. If the antenna is stabilized, the angles will have to
be checked throughout the range of stabilization. When the angles of
incidence exceed the limiting value the contours of the radome must be
adjusted until the upper limit of angle of incidence is not exceeded.

9-24. Structural Design of Radomes. —The thickness and construc¬
tion of the radome wall can be determined on the basis of structural con¬
siderations within limits depending upon the allowable reflection. The
reflection is a cyclic function depending upon the dielectric constants,
thickness of the material, and angles of incidence of the radiation.

There are two basic types of construction: the single plastic or lami¬
nated wall, and the so-called “sandwich” construction involving two or
more materials. The sandwich construction consists of high-strength
skin surrounding a core of lower density, which results in a high-strength,
low-density construction. The sandwich construction also provides a
greater variety of wall construction for high strength and efficient elec¬
trical transmission.

The approach to the structural design problem will depend upon the
shape of the radome and the pressure distribution. These two factors

Sec. 9-25]

EXAMPLES OF RADOMES

317

will determine whether the problem is one of strength or stability. The
stability problem is a difficult one to meet, since no ribs or other means
of reinforcement can be used for the extensive transparent area because
of possible distortion of the electrical pattern.

The design of the mounting of the radome should have due considera¬
tion. Servicing requirements necessitate removal of the radome. The
means of mounting the radome must be quick-fastening as well as strong.

Just as the final proof of a satisfactory aerodynamical and electrical
design are aerodynamical and electrical tests, so structural tests are

Fig. 9-38.—A retractable radome (1) partly extended on a B-29, and the bulge to accom¬
modate the r-f unit (2) aft of the radome.

necessary to assure a satisfactory design, for in a streamlined shape the
calculations can at best be only approximate.

9-26. Examples of Radomes. —Types of radomes vary greatly in size,
shape, and method of construction. Attention is called to a few repre¬
sentative radomes.

Figure 9 38 shows an early type of retractable airborne radome
mounted on a B-29. The radome is a cylinder 35i in. in diameter and
extending about 33 in. when unretracted. While the shape is ideal
electrically, its effect on the speed of the aircraft is most objectionable.

The leading edge of the Eagle vane (Fig. 9T8) is a radome made of
two Fiberglas walls with occasional ribs as spacers. While the airfoil
section is in itself of low drag, the attachment to the plane increases the
drag until it is almost as high as that for the cylindrical radome. This
increase in drag is due to the interference and stagnation points set up by
mounting the airfoil to the plane. An additional feature of this radome
was that it was designed to be deiced by means of hot air. The optimum
wall spacings for heat transfer and for electrical transmission do not
coincide, so that deicing is not very efficient.

A good bombing antenna installation for a B-29 is shown in Fig. 9-39.
This radome houses the antenna shown in Fig. 9-8. The radome extends

Fig. 9-39.—A recent installation on a E-29. Here it is shown extending 7 in.; the
radome was later redesigned to extend 10 § in. to avoid interference between the radiation
and the fuselage.

Figure 911 shows a radome covering an end-fire array. This housing
consists of a thin-walled tube of Laminae and cotton duck. In addition
to protecting the antenna, the housing is used to pressurize the antenna.

The largest airborne installation made during the war is in a TBM
airplane (Fig. 9-40). The radome illustrated, housing the antenna shown
in Fig. 912, is almost 9 ft wide, 3i ft deep, and 13 ft long. Notwith¬
standing its large size it does not seriously alter the performance of the

a minimum amount (about 10^ in. in the final installation), thus present¬
ing a minimum of frontal area. These factors make this installation
aerodynamically superior to those shown in Fig. 9-41 and 9-38. This
radome is made of Fiberglas laminate in a sandwich construction. Its
electrical transmission exceeds 88 per cent for both parallel and per¬
pendicular polarizations through an angle-of-incidence range of 0° to 70°.

318

ANTENNAS, SCANNERS, AND STABILIZATION [Sec. 9-25

Sec. 9-25]

EXAMPLES OF RADOMES

319

aircraft ; two additional stabilizers and a larger motor are all that are
necessary to maintain performance despite the presence of this large
protuberance. This radome depends upon a sandwich wall construction
of Fiberglas laminated skins and Hycar core to give it the desirable elec¬
trical and structural characteristics.

CHAPTER 10

THE MAGNETRON AND THE PULSER

By G. B. Collins, J. V. Lebacqz, and M. G. White

THE MAGNETRON
By G. B. Collins

Strenuous efforts were made by the British, beginning about 1938,
to develop high-power pulsed sources of radiation at very high frequen¬
cies, because of the operational need for microwave radar. Two lines of
attack were followed. One consisted of attempts to improve and modify
conventional types of transmitting tubes, and the other of efforts to
devise entirely new forms of transmitting tubes.

Modifying the conventional type of transmitting tube to satisfy the
requirements of radar met with difficulties. To a first approximation
the electronic characteristics of a low-frequency oscillator or amplifier are
preserved at high frequency only if all dimensions of the tube are scaled
in proportion to the wavelength A; as a result, it is necessary to reduce the
size of tubes as the frequency is increased. The practical consequences
of this become serious as frequencies of 1000 Mc/sec are approached.
The reduction of cathode and plate areas, which under these conditions
vary as A 2 , rapidly reduces the available peak emission and plate dissipa¬
tion. Electrode clearances become so small that they are difficult to
maintain accurately. Although many improvements in the design of
triodes or tetrodes for use at microwave frequencies have been made, the
general limitations just outlined have resulted in greatly reduced effi¬
ciency and power output in the microwave region.

Fortunately, a new type of pulsed microwave generator was invented
whose performance was indeed spectacular. These generators are now
known as “microwave” or “cavity” magnetrons, and they constitute
the most important single contribution to microwave radar. The
description, method of operation, and characteristics of this type of
magnetron are the subject of the first part of this chapter.

As a source of high-power microwaves the multicavity magnetron
represents a very great advance over both the conventional space-charge
and the velocity-modulated or klystron-tube types. A few numerical
comparisons will emphasize this superiority. Above frequencies of
3000 Mc/sec, space-charge tubes such as triodes cease entirely to be
practical sources of r-f power, while magnetrons produce pulse powers

320

Sec. 101]

CONSTRUCTION

321

of the order of hundreds of kilowatts at frequencies as high as 24,000
Mc/sec. The average power output of magnetrons at 3000 Mc/sec is in
the neighborhood of hundreds of watts, or one hundred times that of a
triode operating at the same frequency. Klystrons are very useful
sources of low c-w power at frequencies as high as 24,000 Mc/sec, but
cannot be considered high-power pulsed sources. Their pulse-power
output ranges from a few hundred watts at 3000 Mc/sec to a few milli¬
watts at 24,000 Mc/sec.

Magnetrons are self-excited oscillators and their output does not have
the frequency stability possible at frequencies where power amplifiers
are available and the output frequency is established by crystal-controlled
oscillators. When properly designed and used, they exhibit stability
adequate to the demands of pulse radar.

10-1. Construction. —Microwave magnetrons, or cavity magnetrons
as they are frequently called, are basically self-excited oscillators whose
purpose is to convert the d-c input power into r-f output power. Figures
10T and 10-2 show a particular design of a 10-cm magnetron which is
typical of this class of transmitting tubes. Between the cylindrical
cathode C and anode block A is an interaction space I in which the con¬
version of d-c to r-f power takes place. A constant and nearly uniform
magnetic field is maintained in this interaction space in a direction parallel
to the axis of the tube. In operation, the cathode is maintained at a
negative potential while the anode block is usually at ground potential.
The anode block is pierced in a direction parallel to the axis by a number
of side cavities R which open into the interaction space so that the anode
surface consists of alternate segments and gaps. The ends of the resonat¬
ing cavities open into chambers which are called end spaces, through which
the lines of flux extending from one resonator to the next pass. The
coupling between the resonators is increased (in the design shown in
Figs. 10T and 10-2) by conducting bars called straps S which connect
alternate segments. Power is extracted from one resonator, one method
being the use of a coupling loop L which forms a part of the output cir¬
cuit. The combination of resonant cavities, end spaces, straps, and out¬
put circuit is called the resonant system.

A more detailed discussion of these parts of a magnetron follows.
For pulsed operation, the cathode C is usually oxide-coated and heated
indirectly by an internal heating coil of tungsten or molybdenum. The
cathode structure is attached mechanically to two cathode stems sup¬
ported by glass to provide anode-to-cathode insulation. At each end of
the cathode there is an end shield, or hat H, whose purpose is to prevent
electrons from leaving the cathode structure in a direction parallel to the
axis of the magnetron. These end shields must be kept at a temperature
too low to cause the emission of electrons.

322

THE MAGNETRON AND THE PULSER

[Sec. 10-1

The dimensions of the interaction space depend upon the wavelength
and voltage at which the magnetron is to operate and also upon the
number of resonant cavities, or oscillators. The ratio of cathode diam¬
eter to anode diameter is determined principally by the number of
oscillators, no matter what the wavelength or operating voltage is to be.
For a 12-oscillator magnetron the diameter of the cathode is about one-

H S

Fig. 10*1.—A typical cavity magnetron.

half the anode diameter. For fewer oscillators, it is somewhat smaller
than one-half, and for more than twelve oscillators, somewhat larger.
The anode and cathode diameters for any given type are proportional to
the wavelength and to the square root of the anode voltage.

The particular resonant system shown consists of eight side cavities.
Each of these cavities is similar to a simple oscillating circuit consisting
of a lumped L and C. Although the inductance and capacity of the
magnetron cavity are not strictly lumped, the inductance of the oscil-

Sec. 101]

CONSTRUCTION

323

Iator resides mainly in the circular hole, and the capacitance mainly
between the parallel plane surfaces of the slot. The dimensions of these

4 ? 1

Kyi

Fig. 10-2.—Cutaway view of type of magnetron shown in Fig. 10'1.

cavities determine to a large degree the oscillation frequency of the
magnetron. Since the frequency is a function of the product LC, the same
frequency can be obtained from a variety of shapes which have the

324

THE MAGNETRON AND THE PURSER

[Sec. 10-1

same LC but different L/C. It should be noted that the arrangement of
these cavities is such that for the desired mode of operation their indi¬
vidual C’s are connected in parallel, and so are their individual L’s. Thus
the effective capacitance for the whole magnetron oscillator is NC and the
effective inductance is L/N, where N is the number of resonators. The
frequency of the magnetron is thus nearly that of an individual cavity.
The performance of magnetrons is not very sensitive to the impedance
of the oscillators, L/C, and a wide variety of oscillator configurations are
possible. Three types are shown in Fig. 10-3.

<«> <») (e)

Fio. 10*3.—Magnetron anode blocks, (a) Slot-type magnetron. (6) Hole-and-slot-type
magnetron, (c) Vane-type magnetron.

The simplest is perhaps the slot type (Fig. 10-3a), each of whose
cavities may be thought of as a quarter-wave line (see also Fig. 10-22).
It is a low-impedance oscillator having a large C and small L. The vane
type (Fig. 10-3c), is obviously a high-impedance oscillator, whereas the
hole-and-slot type (Figs. 10-2 and 10-36) usually has an impedance inter¬
mediate between the two. These oscillator configurations were selected
to illustrate some shapes that have been found convenient; the number
of possibilities is unlimited.

Returning to Fig. 10-1 it is seen that the side cavities open at both
ends into chambers, or end spaces. These end spaces assist in coupling
the separate oscillators by allowing magnetic flux to pass from one oscil¬
lator into the next. The straps S consist of rings which are connected
only to alternate segments. The connections are made in such a way
that one set of alternate segments is connected by a strap at one end of
the anode, and the other set of segments is connected by a corresponding
strap at the other end of the anode. Magnetrons may be either single-
or double- (or even quadruple-) strapped, meaning they have either one
or two (or four) straps at each end of the anode. Figures 10-3a, 6, and c
show magnetron anode blocks, without straps; Figs. 10T and 10-2, single¬
ring strapping; and Fig. 10-20, double-ring strapping.

The magnetic field parallel to the axis of the cathode is often produced
by an electromagnet or permanent magnet with pole faces external to the
magnetron. Figure 10-4a shows a typical permanent magnet and a

Sec. 10-2] THE RESONANT SYSTEM 325

magnetron with radial cathode supports. Another type of magnetron
construction, favored for the higher-frequency magnetrons where magnet
weight is of importance, is shown in Fig. 10-45. The construction of such
a magnetron-magnet combination, or “packaged magnetron” as it is
frequently called, is shown in Fig. 10.5. The cathode is usually sup¬
ported axially through iron pole pieces which extend quite close to the

Fig. 10*4.—Two types of magnetron construction: (a) radial cathode and separate mag¬
net; (b) axial cathode with attached magnet.

anode and thus reduce the magnetic field gap. Since the weight of a
magnet which will produce a given magnetic field strength over a given
cross-sectional area increases very rapidly with the length of the gap,
considerable magnet weight can be saved in this manner. It is customary
to supply this type of magnetron permanently attached to its magnet.

10-2. The Resonant System. —In an operating magnetron the charge
distribution in the resonant system produces electric fields which interact
with the space charge in such a way as to sustain the oscillations. Figure
10.6a illustrates such a disposition of charge and electric field at an
instant when the concentration of charge on the ends of the anode seg-

326

THE MAGNETRON AND THE PULSER

[Sec. 10-2

merits is a maximum. One quarter of a period later the electric field and
charges have disappeared and currents are flowing around the inside of
the cavities, producing a magnetic field along the hole portion of the
cavities. Figure 10-66 depicts the currents and fields at this instant.

Fig. 10*5. —Magnetron with axial cathode and inserted pole pieces.

Figure 10-6c shows the charges and electric fields another quarter period
later.

Figure 10-7 is a view of the magnetron opened out in a plane parallel
to the cathode so that the anode faces lie on a plane. The broken lines
show the paths of magnetic flux at the instant shown in Fig. 10-66.

Figures 10-6 and 10-7 illustrate the so-called “ir-mode" in which
magnetrons normally operate; (ir refers to the phase difference between
adjacent anode segments). Actually, the number of possible modes of

328

THE MAGNETRON AND THE PULSER

[Sec. 10-2

oscillation is at least one less than the number of oscillators. Figure 108

Output loop

Fig. 10*7.—View from cathode of anode
block opened out to show longitudinal dis¬
tribution of magnetic field.

shows the distribution of charge
and electric field for a magne¬
tron oscillating in the 7r/2-mode.
A comparison of the electric fields
with those of the tr-mode shown
in Figs. 10-6a, b, and c indicates a
fourfold, instead of eightfold, sym¬
metry, and shows that the field
falls off less rapidly toward the
cathode. Experience has shown
that magnetron operation in any
but the 7r-mode is unsatisfactory.

Possible modes for an 8-oscilla¬
tor magnetron total seven: two ir/ 4-

modes, two tr/2-modes, two 3ir/4-modes, and one tr-mode. In general,
because of differences in the effective inductance and capacity of the

Fig. 10-8.—Distribution of r-f fields and charges in a hole-and-slot anode block oscillating

in the tt/ 2 anode.

oscillating circuits, each of these modes has a different frequency of
oscillation. One of the objectives of magnetron design is to arrange

Sec. 10-2]

THE RESONANT SYSTEM

329

matters so that the electrons excite only the x-mode. Adequate fre¬
quency differences between the desired mode and all others favor stable
operation; in most magnetrons, the frequency of the mode nearest in
frequency is at least 10 per cent greater or less than that of the x-mode.
Unfortunately it has been impossible to design magnetrons that do not
show multiple frequencies under some conditions and this phenomenon
remains as one of the most troublesome encountered in pulsed magnetron
operation.

Fig. 10-9.—Rising-sun magnetron with waveguide output and radial cathode leads.

Power is extracted from only one of the oscillating cavities. This
may be done by means of either a coaxial line output or a waveguide
output. For the coaxial line output, it is usual to insert a loop L (Fig.
10-1) into the inductive portion of one of the oscillators in such a way
that it links the magnetic flux. An r-f potential difference is thus
induced between the ends of the loop, which are connected to the inside
and outside conductors of the coaxial line. This type of output is satis¬
factory for magnetrons whose frequency is 3000 Mc/sec or less. At
frequencies above 3000 Mc/sec a waveguide output is to be preferred as
small coaxial lines arc over and are unduly lossy. Power is extracted
from the back of the cavity by means of a slit which expands, usually
with discontinuities, until its dimensions correspond to those of the wave¬
guide (Figs. 10-9 and 1010).

The magnetrons discussed above are referred to as “strapped”

330 THE MAGNETRON AND THE PULSER [Sec. 10-3

magnetrons. The majority of existing magnetrons are of this type. A
variety of other designs have been constructed, most of which have not
proved to be as satisfactory as the strapped type. One type, however,
has several marked advantages over strapped tubes. It is known as the
“rising sun” magnetron (Figs. 10-9 and 10 10). Mode separation is
accomplished in this design by making alternate resonators of a different

Fig. 1010.—Cutaway view of rising-sun magnetron with axial cathode. The wavelength
is 1.25 cm. (Courtesy oj Bell Telephone Laboratories.)

frequency. It is interesting to note that this resonant system results in
an operating or ir-mode which lies intermediate in frequency between
other modes while, for strapped tubes, the jr-mode has the lowest fre¬
quency. For very high powers, the rising-sun system has considerable
promise. Unlike strapped systems, the rising-sun system permits the
anode to be made with a circumference and a length which are not small
compared to a wavelength without producing mode instabilities. Thus
even at high frequencies large cathodes and large emissions are possible.

10-3. Electron Orbits and the Space Charge. —An electron in the
interaction space of a magnetron is acted on by a constant magnetic field
parallel to the axis of the cathode, a constant radial electric field resulting
from the applied d-c potential, and the varying electric field extending
into the interaction space from charges concentrated near the ends of the

Sec. 10 3] ELECTRON ORBITS AND THE SPACE CHARGE

331

anode segments. In addition, the electron is part of a space charge with
extreme variations in density. The resulting electron motion presents a
problem of extreme complexity, and a detailed theory has not been
developed. A qualitative understanding in simple terms of the processes
responsible for the excitation of the magnetron is, however, possible.

Consider the simple case of a single electron in the interaction space
of a magnetron in the absence of any perturbing r-f fields. In crossed

magnetic and electric fields, there is a force — eE, due to the electric field,

and another, - vxH, due to the magnetic field, where E and H are the

electric and magnetic field strengths, e and v the charge and velocity of
the electron, and c the velocity of light. The resulting motion is approxi¬
mately represented by superposing a slow rotation around the cathode at
nearly constant radius Ro (the Ro rotation), and a faster circular motion
with a smaller radius r 0 (the r 0 rotation). The resultant of these two
motions corresponds roughly to the motion of a point on the circumference
of a wheel as it rolls around a circle somewhat smaller than the cathode
in such a way that its center moves in a circle of radius Ro (Fig. 10T1).
The speed of the slow R 0 rotation is given approximately by the ratio
E/H. The angular velocity of the fast r 0 rotation is determined by H

332

THE MAGNETRON AND THE PULSER

[Sec. 10-3

alone; it is o>o = eH/m. Although the angular velocity of this r 0 rotation
is constant, the magnitude of r 0 depends on the initial kinetic energy of
the electron and may vary for different electrons. The maximum dis¬
tance any electron can proceed toward the anode (Ro + r 0 ) in the absence
of r-f oscillations is fixed by the ratio E/H, and for good operating condi¬
tions is made to be about half of the way from
cathode to anode.

The above description is exact only for the
case of small r 0 (and a particular form of
radial field). The picture is certainly correct
in a qualitative way and this description of the
electron motion may be used in an explanation
of the interaction of the electrons with the
alternating electric fields.

In an oscillating magnetron, the electrons
pass through the r-f fields shown in Figs. 10-6a
and 10-6c, and a change in their velocity re¬
sults. A somewhat unusual fact is that those
electrons which are speeded up have their
radius of curvature reduced and return to the cathode, while those which
are slowed down have their radius of curvature increased and move out
toward the anode.

To make this appear reasonable, let us consider a greatly simplified
case shown in Fig. 10T2. An electron moves through crossed, uniform
electric and magnetic fields with a velocity v that is normal to E and H.
The directions of v, E, and H are made to agree with those acting on the
electron in Fig. 10T1. The force equation is

trons in uniform crossed elec¬
tric and magnetic fields.

Hev ^ . mv 1
- = eli + u

c R

(i)

where R is the radius of the orbit of the electron (R is positive for orbits
curving down). Where the path of the electron is a straight line, the
condition is obtained by letting R = <*>. Equation (1) then reduces to
v = Ec/H. Inspection of Eq. (1) also show's that for v < Ec/H, the
electromagnetic force will be reduced and the electrons will be deflected
in the direction of the electric force. For v > Ec/H, the deflection will
be in the direction of the magnetic force. The deflection that an electron
suffers in this example when speeded up or slowed down thus corresponds
to what happens in a magnetron and it is significant that the operating
conditions are ones for which v ~ Ec/H. This example is given only to
illustrate the complex electronics of these tubes and is obviously inac-

Sec. 10 3] ELECTRON ORBITS AND THE SPACE CHARGE

333

charge. The fields in a magnetron, however, are certainly such as to
produce this separation of fast and slow electrons.

The problem is shown in more detail in Fig. 1013. Consider an
electron at point A at the instant for which the fields are as shown. The
r-f field at this point tends to speed up the electron. As it speeds up, the
radius of curvature of its path is decreased, and it will move along a path
corresponding to the solid line and strike the cathode with appreciable

energy. This electron is thus removed from the space charge, and plays
no further role in the process except perhaps to produce a few secondary
electrons from the cathode. An electron at point B, however, is in a
decelerating r-f electric field. As a result of the reduction in electron
velocity, the radius of curvature of its path is increased. If the fre¬
quency of oscillation is appropriate, this electron will always be in a
decelerating field as it passes before successive anode segments. The
result is that the electron, following a path of the type shown, eventually
strikes the anode. Because of retardation by the r-f field, the electron
gives up to the r-f field the energy gained in its fall through the d-c field
to the anode.

Since the electron moves from the cathode to the anode in a very
small number of oscillations, the condition that the electron keep step,

334

THE MAGNETRON AND THE PULSER

[Sec. 10-3

in its course around the cathode, with the variations of r-f oscillations
need not be satisfied exactly. Electrons once in step with the r-f field
remain in this state long enough to get to the anode, even if their angular
velocity is not exactly correct. This explains why the operating condi¬
tions of magnetrons are not very critical with respect to the magnetic
field, anode voltage, or other quantities which might affect the velocity
of the electrons.

Fig. 10-14.—Space charge in nonoscillating magnetron.

Appreciable energy is associated with the r 0 rotation. This motion
takes place, however, in a substantially constant r-f field, since the Ro
rotation keeps the electron in step with the variations of the r-f field.
As a result, the r-f field has little or no effect on the energy associated
with the r 0 rotation.

This qualitative picture shows how those electrons whose initial phase
relationship is such that they absorb energy from the r-f field are elimi¬
nated at once from the space charge. Such electrons strike the cathode
in the course of the first r 0 period. On the other hand, electrons which
leave the cathode at such a time and place that they transfer energy to
the r-f field continue around the cathode in a cycloidal path which
expands toward the anode, transferring to the r-f field the energy they
gain from the d-c field.

Sec. 10 3] ELECTRON ORBITS AND THE SPACE CHARGE

335

It must again be emphasized that the above description is correct in
terms of general principles, but the detailed picture is doubtless more
complicated. One experimental fact difficult to explain is the extra¬
ordinarily high electronic efficiencies of some magnetrons: up to 85
per cent.

In addition to describing the paths taken by individual electrons
in the interaction space, it is helpful to consider the behavior of the space

charge as a whole. In the absence of s-f fields, the space charge forms a
rotating cylindrical sheath around the cathode extending out about half¬
way to the anode (Fig. 10-14). The above reasoning suggests that, under
the influence of the r-f fields, the electrons in this space charge which are
in an accelerating r-f field travel back toward the cathode, while those in
a decelerating r-f field travel toward the anode.

The result may be seen from Fig. 10-15. The rotating cylindrical
sheath is distorted (for an eight-oscillator magnetron) into a smaller
cylinder with four spoke-like ridges running parallel to its axis. This
space charge configuration rotates with an angular velocity which keeps
it in step with the alternating r-f charges on the anode segments, and
the ends of these spokes may be thought of as brushing by the ends of the

336

THE MAGNETRON AND THE PULSER

[Sec. 10-4

anode segments and thus transferring charge from the cathode to the
anode.

The r-f current set up in the oscillators is principally a displacement
current produced by this rotating space charge. As the spokes of the
negative space charge pass in front of an anode segment, a positive charge
is induced on its surface. Half a period later, this positive charge has
flowed around the back of the two adjacent oscillators to the two adjacent
anode segments and the spoke of the space charge has rotated to a posi¬
tion in front of the next anode segment.

In addition to these displacement currents, conduction currents are
produced by the flow of electrons from space charge to the anode. Elec¬
trons arrive at the anode at such a time as to constitute a conduction
current approximately 90° out of phase with the r-f voltage, and thus
have little effect on the oscillations.

10-4. Performance Charts and Rieke Diagrams.—Four parameters
determine the operation of the magnetron; two are associated with the
input circuit, and two with the output circuit. A typical set is 77, I, G,
and B. 77 is the magnetic field, 7 is the anode current, and G and B are
the real and the imaginary parts of the r-f load on the magnetron meas¬
ured at some arbitrary point in the output line. The observed quanti¬
ties are three in number, usually power P, wavelength X, and voltage V.
The problem of presenting these observed quantities in terms of the four
parameters is greatly simplified by the fact that the input and output
parameters operate nearly independently of one another. Thus, it is
possible to keep G and B (the load) fixed, and study the effect of 77 and I
on P, X, and V with the assurance that the nature of the results will not
be greatly altered by changes in G and B. Conversely, H and I may be
fixed and the effect of G and B on P, X, and V observed. As a result of
this situation, it is customary to present the operating data on two graphs.
One is called the “performance chart,” and shows the relationship
between H, I, V, P, and X for constant load; the other is called a “Rieke
diagram,” and shows the relationships between G, B, P, X, and V for
constant 7 and 77.

Figure 10-16 is a performance chart for a typical magnetron with a
frequency of about 2800 Mc/sec.

It has been customary to plot anode voltage V as ordinate, and cur¬
rent 7 as abscissa. On such a graph the lines of constant 77 are more or
less parallel and slope upward to the right. Thus (referring to Fig.
10-16), if the magnetron is operated at a constant magnetic field, say
2100 gauss, the relations of voltage and current are given by points on
the 77 = 2100 gauss line. (At 20 kv, the current drawn will be 48 amp.)

On the same chart are plotted the lines of constant power output.
These are the solid lines whose form suggests hyperbolas; they show the

Sec. 10-4] PERFORMANCE CHARTS AND RIEKE DIAGRAMS

337

pulse r-f power which is obtained under varying input conditions. Thus
at 20 kv and 48 amp, the power output is 470 kw. This same power can
also be obtained at 25 kv and 30 amp with a magnetic field a little less
than 2700 gauss.

In addition, it is customary to add curves of constant efficiency
obtained directly from the above data. These lines of constant efficiency
are the dotted lines looping up and to the right on the diagram.

0 10 20 30 40 50 60 70 80

Current in amperes

liG. 10-1G. Typical performance chart of a magnetron (4J31?. Irequency is expressed
in terms of difference from a base frequency.

It is possible to add to this chart lines of constant frequency, so that
the variation of frequency with input parameters may he studied. This
information is useful in establishing limits on the variation of current
during a pulse. (See the treatment of pulse length limitations in Sec.
10-5.1 The dashed lines in Fig. 10-10 are contours of constant frequency.
In this case, for currents greater than 40 amp, they are nearly parallel to
the lines of constant magnetic field; this is an ideal condition, since
changes in current produce no change in frequency.

Performance charts like that shown in Fig. 10-10 are indispensable

338

THE MAGNETRON AND THE PULSER

[Sec. 10-4

in the selection of proper operating conditions for a magnetron. The
input voltage, input current, and magnetic field are chosen by making a
compromise among such factors as peak power output, efficiency, allow¬
able magnet weight, input impedance, and stability of operation. All
the necessary information can be obtained from a good performance chart.

0 ^50 -Pulse power in kw

-Frequency in Me/ sec

Fig. 10*17. —Rieke diagram of a magnetron. The circles to the right and left of center are
transformed VSWR = 1.5 circles.

It is advisable to select an operating point that is not near regions of
anomalous behavior. At low currents (below 15 amp, Fig. 1016), or at
excessive powers (above 800 kw, Fig. 10T6), instability is likely to occur.
Below 1700 gauss the efficiency is obviously unsatisfactory. Considering
Fig. 1016 as an example, the operating point should be between 30 and
60 amp and 17 and 25 kv.

For magnetron-magnet combinations (Fig. 10*4), the magnetic field
is fixed by the tube manufacturer, and the performance chart is reduced
to a single magnetic-field line on a general performance chart. In such
a case, it is only necessary to establish an operating voltage or current.

Sec. 104] PERFORMANCE CHARTS AND RIEKE DIAGRAMS

339

The performance of a magnetron in terms of its output parameters,
or r-f loading, is presented on a Rieke diagram (Fig. 10T7). It would
appear useful to express the r-f loading in terms of the resistance and
reactance presented to the magnetron at the output loop. Since these
quantities are difficult to determine experimentally, the Rieke diagram
is a compromise between these quantities and others which can be
obtained with ease experimentally. At microwave frequencies, it is
customary to determine the constants of a load by observing the phase
and magnitude of the standing waves set up by it, and the Rieke diagram
is designed to use these experimental data directly. Since it is imprac¬
tical to determine the r-f loading at the output of the magnetron, an
arbitrary point in the output circuit is selected to which all measurements
can be referred. The desired range of r-f loading is obtained by adjusting
a tuner until the desired phase and magnitude of standing waves is indi¬
cated by a sliding pickup probe. 1 The independent variables VSWR p
and phase <j> are used as coordinates of a polar diagram. Power output
and frequency are measured for various points on the diagram, and the
data used to construct contours of constant frequency and constant
power.

Magnetron manufacturers usually furnish diagrams such as this for
every tube type, and these give information of considerable importance
to system designers. Consider the effect of presenting such a mismatch
to the magnetron that a VSWR of 2 results, and suppose further that the
phase of this mismatch is such that the voltage minimum corresponds to
point A (Fig. 10-17). The result will be a power output for the specified
input conditions of about 650 kw. If the phase of the VSWR is changed,
say by increasing the line length between the magnetron and the mis¬
match until point B is reached, the power output falls to 425 kw. The
efficiency of the magnetron at point A is thus 50 per cent greater, but
operation at this loading is unsatisfactory for another reason. As repre¬
sentative of a general class of load instability, consider a change in phase
angle about the loading A of +7-5° (dotted arrows) which might result
from the turning of an imperfect rotary joint. The power output will be
essentially unaltered, but a maximum change in frequency of 12 Mc/sec
occurs. If a heavy loading corresponding to point A is used, frequency
shifts of this magnitude, and greater, are frequently encountered and may
seriously affect the system operation. At point B, however, correspond¬
ing to light loading, a phase shift of ±7.5° results in only a 3 Mc/sec fre¬
quency shift. This illustrates the compromise that must be made
between efficiency and frequency stability. Magnetrons are usually
designed with an output coupling such that the center of the Rieke

1 See Technique of Microwave Measurements, Vol. 11, Radiation Laboratory Series,
Sec. 2-5; see also Sec. Il l of this volume.

340 THE MAGNETRON AND THE PULSER [Sec. 10-5

diagram, which corresponds to a matched load, represents a reasonable
compromise between efficiency and frequency stability.

It is possible to adjust the loading on the magnetron to any reasonable
value by the suitable use of r-f transformers (Sec. 11-1) in the output line.
As an example, suppose it is desirable to operate the magnetron repre¬
sented by Fig. 10-17 at a point of high efficiency and low frequency
stability corresponding to point A. This can be accomplished by intro¬
ducing a transformer which sets up a 2-to-l VSWR and making its dis¬
tance from the magnetron such that the phase of this VSWR corresponds
to point A. By moving this transformer along the line in either direction
one-quarter wavelength, operation corresponding to point B can be
obtained. In comparing the effect of different loads corresponding to
various points on the Rieke diagram, it should be realized that these
points represent transformations that reduce the size of a circle of con¬
stant VSWR as its center is moved away from the center of the diagram.
In Fig. 1017 the circles about points A and B represent the VSWR = 1.5
circle when displaced different distances from the center of the diagram.

The load points A and B, with their associated variations in load in
the above example, are especially simple cases. In general, the load
variations correspond to a very irregular path on the Rieke diagram
whose behavior is unpredictable. A safe policy in design is to estimate
the maximum variation in VSWR to be expected from the r-f circuits, and
to employ a loading of the magnetron which does not produce a frequency
change too large to be accommodated by the radar receiver even when
this variation in VSWR is of such a character as to produce the maximum
possible frequency shift.

Appreciation of the effects of the r-f load on the performance of mag¬
netrons has contributed more than any other single factor to magnetron
reliability. As a corollary, it is also true that many troubles attributed
to magnetrons result from a failure to use properly the information pro¬
vided by a Rieke diagram.

10-5. Magnetron Characteristics Affecting Over-all Systems Design.

One of the shortcomings of microwave magnetrons is their limited
adaptability to different requirements. This circumstance has forced
the design and production of an extremely large number of tube types.
Although the development of microwave magnetrons in this country
began only in late 1940, there now exist over 100 distinct types of mag¬
netrons, despite early and continuing attempts at standardization.
During the past war it was true, almost without exception, that each new
radar system made new demands on the magnetron and required the
development and production of a new type. This has not been necessary
in the case of conventional types of tubes, since the associated circuit
elements which are largely responsible for over-all performance lie exter-

Sec. 10-5]

MAGNETRON CHARACTERISTICS

341

nal to the tube and are accessible to change. In microwave magnetrons,
the circuit elements are an integral part of the tube and must be incor¬
porated with great care into every new design.

Thus any radar system designed to meet a new set of conditions or to
operate on a new frequency will require the development of a new mag¬
netron type, or at least a critical evaluation of the characteristics of
existing types. Since the over-all characteristics of the radar system
are so closely related to, and restricted by, the performance of the mag¬
netron, a- general knowledge of the important characteristics of magne¬
trons is essential.

Listed below with a discussion of each are the characteristics of
magnetrons of particular importance to system design. These charac¬
teristics are not usually independent of one another and their relation¬
ships are also considered.

Wavelength Scaling .—Since the wavelength of the radiation from a
magnetron is fixed or at best variable over a limited range, operation on
different wavelengths requires different tubes. To a first approximation,
magnetrons of different wavelength are derived from one another by a
simple over-all scaling process. All essential dimensions of the tube are
altered by the scaling factor a = X/X 0 , where X is the new wavelength
desired and X 0 is the wavelength associated with the original dimensions.

If this is done, the new tube at wavelength X will operate at the original

voltage and current, and at a magnetic field H = ^ // 0 , where H o is the

operating magnetic field of the original magnetron. The power input,
and thus the power output, increases with increasing wavelength. A
rough rule is: The ■pulse power output (or input ) of scaled magnetrons
varies as the square of their wavelength. The change in the size of the tube
with wavelength is the basis of this rule. The pulse power input is often
limited by cathode emission and, since the cathode area is proportional
to X 2 , pulse power input is also proportional to X3. Similar reasoning
shows that if the pulse power output is limited by r-f voltage breakdown
Within the tube, the same variation of power with wavelength is to be
expected.

This rule is an important one from the standpoint of system design.
At any given time it may not be exact, because special emphasis may
have been given to obtaining high peak powers at a particular wave¬
length and a better design evolved as a result. In the long run, however,
the validity of the rule is reestablished, because any new design can,
within limits, be used to advantage at other wavelengths.

Pulse Power .—The most outstanding characteristic of pulsed micro-
wave magnetrons is their extremely high pulse power output, made
possible by the very large emission yielded by oxide cathodes when pulsed,

Pulse power output in kw

342

THE MAGNETRON AND THE PULSER

[Sec. 10-5

and the high efficiency of magnetrons even at very short wavelengths.
The pulse powers available extend over a range of 10 5 (0.02 kw to 2000
kw).

Fig. 10-18.— Diagram showing power and frequency distribution of representative micro¬
wave magnetrons developed up to 1945.

The demands of microwave radar resulted in a rather extensive
development of magnetrons whose frequencies are concentrated more or
less into two bands. Figure 10T8 shows on a logarithmic chart the fre¬
quency and pulse power of magnetrons that have been produced in

Sec. 10 5]

MAGNETRON CHARACTERISTICS

343

appreciable numbers and thus constitute well-tested designs. Fixed-
frequency tubes are indicated by a dot and tunable tubes by a line whose
length shows the tuning range. Whenever possible the magnetrons are
identified by their RMA type numbers.

The values of pulse power given in this chart are conservative ones
corresponding to reliable operating conditions. Pulse powers consider¬
ably in excess of those given for the highest power tubes have been

Fio. 10-19.—An array of anode blocks showing the effect of wavelength and pulse
power output. Top row—10 cm, pulse power 2500 to 0.1 kw; second row—3 cm, pulse
power 600 to 0.025 kw; single block—1.25 cm, 80 kw.

observed. At 3000 Mc/sec, for example, 4500 kw have been obtained
from the HP10V, and the British report 3700 kw peak at an average
power level of 5 kw from a similar tube, the BM735.

The general rule that maximum pulse power is proportional to wave¬
length squared is illustrated by the falling-off of power at high frequencies.
Exceptions to this rule are the magnetrons in the 20- to 30-cm range,
whose pulse power output is not as high as might be expected. This
particular situation resulted from a lack of need for very high powers in
this wavelength range.

Figure 10T9 illustrates the effects of wavelength and power output on
the design of anode blocks. In the top row, from left to right, are 10-cm
anode blocks for magnetrons with pulse power outputs of 2500, 1000,
250, 5, and 0.1 kw. The reduction in anode diameter with pulse power
is evident. In the second row are 3-cm anode blocks with pulse power

344 THE MAGNETRON AND THE PULSER [Sec. 10-5

outputs of 600, 200, 80, and 0.025 kw. The single anode block at the
bottom is from a 1.2-cm 80-kw rising-sun magnetron. Figure 10-20
shows one variety of a high-power (1000-kw output) magnetron. This
design has a rather long anode with heavy double-ring straps and a
coaxial output.

Fio. 10-20.—A high-power magnetron (type 720); 10 cm, 1000-kw pulse power output.

(Courtesy of Bell Telephone Laboratories .)

Average Power .—In Sec. 10-2 it was stated that the cathodes of oscil¬
lating magnetrons are subjected to back bombardment by some of the
electrons in the surrounding space charge. This bombardment produces
heating of the cathode surface which amounts to about 5 per cent of the
average power input to the magnetron. If this back-bombardment
power exceeds the normal heater power of the cathode (which is fre¬
quently turned off while the magnetron is oscillating) abnormally short
tube life results. Back bombardment usually limits the average power
output. This limit can be raised by designing cathodes with very large
thermal dissipation, but the average power of magnetrons designed for
radar use rarely exceeds 0.2 per cent of the pulse power output. Table

Sec. 10 5]

MAGNETRON CHARACTERISTICS

345

10-1 shows the average and pulse power output of selected magnetron
types representing the microwave range of frequencies.

Table 10T.— Average and Pulse Power Outputs of Microwave Magnetrons

RMA
type No.

Frequency,

Me /sec

Maximum
average power
output, w

Pulse power
output,
kw

Maximum pulse
length,
fisec

4J21

1,180

800

6.0

4J73

3,100

600

1000

2.5

725

9,400

2.5

3J21

24,000

0.5

Efficiency .—The purpose of a magnetron is to convert d-c power into
a-c power at very high frequencies. Magnetrons can perform this con¬
version with an efficiency as high as 85 per cent, which compares favorably
with the efficiency of d-c to 60-cps a-c converters. Magnetron efficien¬
cies customarily lie between 30 and 50 per cent.

The output efficiency is the product of what is called the “electronic
efficiency” and the “circuit efficiency.” The electronic efficiency is the
fraction of the d-c energy input which the electronic space charge converts
into r-f energy. The circuit efficiency is the fraction of the r-f power
going into the resonant system which appears as output power; the
remainder is wasted as heat because of copper losses. Electronic effi¬
ciencies depend on the magnetic field, on r-f loading, and on the cathode-
to-anode radius ratio. Electronic efficiencies of about 70 per cent are
realized over a very large range of frequencies. Circuit efficiencies
depend on the frequency, since this determines the conducting skin depth
which in turn governs the copper losses. The C/L ratio of the resonators
and the r-f loading also affect the circuit efficiency. Circuit efficiencies
for the usual r-f loading vary from close to 100 per cent for the 1000-
Mc/sec range to 50 per cent for the 25,000-Mc/sec range.

Realization of high magnetron efficiency affects system design in two
ways. High efficiency accompanies high magnetic fields which require
heavy magnets. Higher efficiencies can also be obtained by closer
coupling (Sec. 10-4), which at the same time decreases the frequency
stability. Experience has shown that it is expedient to provide sufficient
magnetic field for obtaining good efficiencies even at the expense of some
increase in weight. The variation of efficiency with magnetic field can
be found from the performance chart. As discussed in Sec. 10-4, con¬
siderable efficiency should be sacrificed for the sake of frequency stability.
The relationship of these two quantities can be obtained from a Rieke
diagram.

346

THE MAGNETRON AND THE PULSER

[Sec. 10-5

Pulse Voltage .—The input impedance 1 of most pulsed magnetrons lies
between 700 and 1200 ohms. For example, magnetrons with an input
of 260 kw (100-kw output) require a pulse voltage of about 15 kv; inputs
of 2500 kw (1000-kw output) require 30 kv, and one magnetron designed
for 6000-kw input (2500-kw output) requires a pulse voltage of 50 kv.

Serious attempts have been made to design magnetrons that would
operate at lower input impedances because such tubes would simplify the
design of line-type pulsers. These attempts have been unsuccessful, and
350 ohms was the lower limit in mid-1946. The design of magnetrons
with high impedances is, however, easily achieved, and tubes with input
impedances as high as 10,000 ohms have been produced. Table 10-2
shows the input pulse power, pulse voltage, and input impedance of
existing 10-cm magnetrons with input pulse powers ranging from 2 to
6000 kw. Power outputs can be estimated by assuming an efficiency
of 40 per cent.

Table 10-2.—Input Characteristics of Microwave Magnetrons

Tube No.

Input pulse
power, kw

Pulse voltage,
kv

Input impedance,
ohms

4J60

1.5

1125

2J38

1000

2J32

250

900

4J31

2500

360

HP10V

415

By varying the magnetic field in which the magnetron operates, any
given design can be made to operate satisfactorily over a range of pulse
voltage of roughly 50 per cent. For satisfactory operation, however, the
tube will exhibit about the same input impedance values. Exact figures
can be obtained from performance charts.

Pulse-length Limitations .—The early experiments of the British with
high-power pulse techniques revealed a characteristic of oxide cathodes
which is responsible in large measure for the high pulse power of magne¬
trons. It was found that under pulsed conditions oxide cathodes can
emit as much as 20 amp/cm 2 as compared to about 0.2 amp/cm 2 for
d-c emission.

More recently, currents as high as 100 amp/cm 2 have been obtained.
This current is carried partly by primary electrons and partly by sec¬
ondary electrons liberated from the oxide cathode by back bombardment.

1 The word impedance , as used in this section, means the voltage-current ratio of a
magnetron at the operating point. The dynamic impedance , the slope of the voltage-
current curve near the operating point, is very much lower, usually around 100 ohms.
See Sec. 10-8.

Sec. 10 S]

MAGNETRON CHARACTERISTICS

347

Whatever the source of the emission, if too large a current is drawn for
too long a time, sparking and other instabilities result. The exact
relationship between peak cathode emission and pulse length depends
on the type, temperature, and age of the cathode. To a fair degree of
approximation, the maximum permissible peak emission varies inversely
as the square root of the pulse length: ~ l/v7- Thus a cathode

which will emit 20 amp for a pulse duration of 2 /tsec will probably emit
40 amp during a 0.5-psec pulse. In consequence, greater energy per pulse
can safely be obtained for the longer pulses.

Pulse durations greater than 5 /isec are rarely employed when magne¬
trons are used as transmitter tubes. Frequency modulation during the
pulse becomes a serious problem for longer pulses, even if sparking
troubles are overcome. Pulse durations as short as 0.25 /isec have been
used successfully, particularly with high-frequency magnetrons whose
starting times are short.

Tuning of Magnetrons .—To change the frequency of a magnetron
more than a few megacycles per second requires that a change be made
in the resonant circuits of the anode. Either the effective capacity or
effective inductance must be varied, and, since the resonant circuits are
within the evacuated portion of the tube, variation of either of them is a
troublesome problem.

For this reason early magnetrons were not tunable, and only a later
need for increased flexibility of radar systems forced the design of tunable
tubes. The practical advantage of tunable over fixed-tuned magnetrons
is obvious. If operation on a number of frequencies is contemplated, a
single tunable magnetron can replace a whole set of fixed-frequency
magnetrons, and only with a tunable magnetron is it possible in general
to obtain r-f power at a specified frequency. The performance charac¬
teristics of tunable magnetrons are equivalent to those of the correspond¬
ing fixed-frequency tubes, and there is thus no reason, except availability,
for not using them.

Tuning of the higher-frequency microwave magnetrons is accom¬
plished by inserting conducting cylinders into the inductive portion of
each resonant cavity, thus decreasing the effective inductance. This
construction, shown in Fig. 10-21, provides a tuning range as high as 12
per cent.

At frequencies lower than about 5000 Mc/sec, the magnitude of the
longitudinal displacement required in inductive tuning becomes incon¬
venient, and other tuning methods are adopted. Figure 10-22 shows a
“C-ring” type of tunable magnetron, in which a conducting surface can
be moved toward or away from the straps and capacitive portion of the
resonant cavities, thus changing their effective capacity. The disad-

348

THE MAGNETRON AND THE PULSER

[Sec. 10-5

vantage of this method is that sparking may occur within the tuning
arrangement at high pulse powers.

An unsymmetrical type of tuning which has advantages for high-
power operation is shown in Fig. 10-23. The frequency of the single
tuning cavity is changed by distorting the diaphragm. Since the tuning
cavity is tightly coupled to one of the resonant cavities, and since all the

FiG. 10-21.—Magnetron with sprocket tuning. The change in frequency is accomplished
by changing the inductance of the resonators.

resonant cavities are very closely coupled to one another by the straps,
the oscillating frequency of the entire magnetron is altered. This unsym¬
metrical type of tuning distorts the electric field patterns within the
magnetron and therefore limits its effective tuning range to about 6 per
cent. Advantages of the method are its mechanical simplicity and its
ability to handle very high pulse powers. Figure 10-24 shows output
power as a function of tuning adjustment.

Various other tuning schemes have been tried, and still others will be
devised, but the three types described above represent the basic methods.

Wartime experience with radar demonstrated that tunability was very
desirable but that extreme tuning range was not.

Sec, 10 5]

MAGNETRON CHARACTERISTICS

349

Frequency Pulling by the R-f Load. —Magnetrons are self-excited
oscillators whose frequency depends on output loading. In the process
of scanning by the radar antenna, it is inevitable that variations in the
magnetron loading will occur as a result of changing reflections from
rotary joints, antenna housings, and large near-by reflecting objects.
Such changes in loading produce changes in frequency which may be

L_ __ ___J

Fio. 10-22.—Cutaway view of a 1000-Mc/sec tunablfe magnetron showing the C-ring tuning
mechanism and the slot-type resonators. (Courtesy of Bell Telephone Laboratories.)

large, and this phenomenon is a source of considerable trouble. It
necessitates careful engineering of the entire r-f system from magnetron
to antenna, and also affects receiver design.

The problem is attacked in three ways: (1) the magnetron is designed
so that its frequency change with changing r-f loading is small; (2) the
variations in r-f loading are reduced by careful design and construction
of the r-f components; (3) the radar receiver is made insensitive to changes
in frequency by making its pass band broad or by incorporating automatic
frequency control. It is the purpose of this subsection to discuss only
the first of these methods of attack, that is, magnetron design.

The effect of loading on the frequency of a magnetron is usually
expressed by what is called the pulling figure, which is defined as the total
frequency excursion which results when a standing-wave ratio of 1.5 in voltage

350

THE MAGNETRON AND THE PULSER

[Sec. 10-5

is presented to the magnetron and varied in phase over at least a full half cycle
(see Fig. 10-17). The VSWR of 1.5 was selected for this definition since
it is in the range usually encountered in radar systems. Pulling figures
for magnetrons with comparable loading increase with frequency, since
the same fractional change in frequency corresponds to a larger number

Fig. 10-23. —Magnetron with unsymmetrical tuning cavity.

of megacycles at higher frequencies. Thus, similar magnetrons at 3000,
10,000, and 30,000 Mc/sec w-ould have pulling figures of, say, 5, 16, and
50 Mc/sec. Since receiver bandwidth is not changed substantially as
the radar frequency increases, frequency stability becomes a more
important consideration at shorter wavelengths.

The effect of loading on frequency stability and methods of obtaining
various loadings have been considered in Sec. 10-4. As stated there, the
requirements of any system usually make necessary some sort of com-

Sec. 10-5]

MAGNETRON CHARACTERISTICS

351

promise between efficiency and frequency stability and this compromise
is arrived at from a study of the Rieke diagram.

It is possible in some cases to combine with the magnetron proper a
high-Q cavity coupled to it in such a way as to reduce the pulling figure
by a large amount with little or no loss in efficiency. The ratio of the
pulling figures with and without the high-Q cavity for equivalent operat¬
ing conditions is called the “stabilization factor,” which may be as large
as 10 but is usually between 2 and 5. The addition of this stabilizing

Frequency in Mc/sec

20 .

</)

20 !

Fio. 10-24.—Characteristics of the 4J70 series.
Magnetic field = 2700 gauss
Pulse current = 70 amp
Pulse duration = 0.8 nsec
PRF = 400 pps.

cavity has the disadvantage, however, of reducing the tuning range of
the magnetron; further, it may aggravate mode instabilities. If con¬
stant-frequency operation is required, stabilized magnetrons should be
seriously considered.

Frequency stabilization has been incorporated into only a few mag¬
netrons. A good example is the 2J41, which has a pulse power output of
500 watts at 9310 Mc/sec and a pulling figure of 1.5 Mc/sec with a
tuning range of 0.7 per cent. The stabilization factor is 10. The 10-cm
series 4J70 to 4J77 is stabilized by a factor of 1.5 and the 1.25-cm 3J21
by a factor of 2. High-power magnetrons with high stabilization have
not been developed.

Weight .—The development of airborne radar placed great emphasis
on the reduction in weight of all components. As a result, magnetron-
magnet combinations were produced in which every effort was made to
reduce the total weight. This development has been so successful, par¬
ticularly for the higher-frequency magnetrons, that the weight of a

352

THE MAGNETRON AND THE PULSER

(Sec. 10-6

magnetron-magnet combination is now a small fraction of the weight of
the pulser required to drive it. The weight of magnetrons and their
magnets has thus ceased to be a critical design consideration.

10-6. Magnetron Characteristics Affecting Pulser Design. —The
magnetron, standing as it does between the pulser and the r-f system,
imposes restrictions on the design of both these components. Pulser
design in particular has been complicated by some very strict require¬
ments which the magnetron places on pulse shape and voltage regulation.
These requirements arise from undesirable magnetron characteristics
which it has so far been impossible to remove in the design of the tubes.
They may perhaps be eliminated from magnetrons in the future.

The stringency of the conditions that the magnetron places on the
pulser or on the r-f components increases rapidly as the maximum operat¬
ing conditions are approached. Thus the surest way to obtain reliable
performance is to operate the tubes at conservative ratings.

Little need be said here about the interaction between the magnetron
and the r-f components. The relationship between frequency stability,
VSWR of the r-f system, and the magnetron pulling figure has been
covered in Sec. 10-4. The related subject of long-line effect is discussed
in Sec. 1T1. 1

Because the interaction between the pulser and the magnetron has
only recently been understood, many serious difficulties have been
alleviated in the past by the unsatisfactory process of cut-and-try. Four
characteristics of magnetrons are largely responsible for these troubles.

Change of Frequency with Current .—The input impedance of a mag¬
netron varies with voltage as shown in Fig. 10-29. The average input
impedance is usually in the range of 400 to 1000 ohms. Very small
changes in anode potentials produce large changes in anode current.
For example, the performance chart of a 4J31 magnetron (Fig. 1016)
shows that, at a magnetic field of 2300 gauss, a change of voltage from
20 kv to 22.5 kv causes a change in current from 20 to 50 amp. Varia¬
tions in voltage during a pulse must be kept within small limits to prevent
large current variations and consequent distortion of the r-f pulse shape.

The rate of change of frequency with anode current, dv/dl, deter¬
mines the amount of frequency modulation and undesirable distortion
in the energy spectrum of the pulse which will be caused by current
variation during the pulse. In the usual operating range for most mag¬
netrons, dv/dl is about 0.1 Mc/sec per amp, but it can be as large as
+1 Mc/sec per amp. The exact value depends to a considerable degree
on the operating point selected. To illustrate this problem, consider a
magnetron with dv/dl = 0.4 Mc/sec per amp driven by a 1-^sec pulse
which “droops” from 55 to 50 amp. This 5-amp change in current will

1 See also Microwave Magnetrons, Vol. 6, Sec. 7-2, Radiation Laboratory Series.

Sec. 10-6]

MAGNETRON CHARACTERISTICS

353

produce a frequency modulation of 5 amp X 0.4 Mc/sec per amp =
2 Mc/sec. Since the bandwidth of the receiver for a l-^isec pulse would
be about 2 Mc/sec, frequency modulation of this magnitude will result
in a serious loss of received energy. When longer pulses and correspond¬
ingly narrower bandpass receivers are used, this problem becomes much
more critical and may place very severe requirements on the flatness of
the current pulse.

Instabilities .—It has so far been found impossible to construct mag¬
netrons that do not occasionally present to the pulser either a very low
impedance as a result of a gas discharge (sparking) within the tube, or a
very high impedance due to a failure of the magnetron to oscillate in the
proper manner (mode-changing). Either of these events may occur only
once or twice per million pulses, but when such an event does take place,
voltage and current surges are frequently produced in the pulser which
may cause failure of some component. The pulser designer must there¬
fore over-design components and provide special protective circuits to
guard against events that may happen only once in a million pulses. All
magnetrons change mode or spark occasionally, but the frequency of
sparking or mode-changing can be reduced by operating at moderate peak
anode currents and short pulse durations. Magnetron performance and
life are materially increased if the pulser design is such that, in the event
of sparking or mode-shifting, an excessive discharge does not take place
through the magnetron.

These two types of instability, mode-changing and sparking, are diffi¬
cult to distinguish in practice, since mode, changing usually produces
sparking and vice versa. In spite of this, it is advantageous to consider
them separately since the cure for each is quite specific and distinct.

Sparking is an internal discharge in the magnetron which arises as a
consequence of the generation of bursts of gas within the tube. The
gas may be liberated from the anode or from the cathode; in either event
the frequency of the phenomenon is multiplied by an increase in anode
voltage, anode current, or pulse length. Operation of a magnetron under
•conditions which exceed specifications for any of these quantities results
in a very rapid increase in sparking rate. Sparking limits the maximum
pulse length at which magnetrons can be operated.

Of all the modes of oscillation possible in magnetrons, only the ir-mode
is ordinarily used but all magnetrons will sometimes oscillate in an
unwanted mode, or alternate erratically between two modes. This
tendency is responsible for some of the most troublesome problems in
magnetron and pulser design. Considerable progress toward an under¬
standing of the phenomenon has now been made, 1 and when mode-

1 F. F. Rieke and R. Fletcher, “Mode Selection in Magnetrons,” RL Report No.
809, Sept. 28, 1945. Microwave Magnetrons ) Vol. 6, Chap. 8, Radiation Laboratory
Series.

354

THE MAGNETRON AND THE PULSER

[Sec. 10-6

changing difficulties arise a systematic attack is possible. The important
conclusions of this study are given here.

Mode changes are of two types. One type is caused by anode currents
so high that they exceed the conditions for oscillation and cause transition
into a state of nonoscillation or into another mode of oscillation. The
second type arises from a failure of the oscillations in the desired mode to
build up rapidly enough with respect to the voltage rise at the start of the
pulse. The first type is encountered usually in lower-power c-w magne¬
trons, rarely in pulsed tubes. The
second type, called “mode-skip¬
ping,” is common to nearly all high-
power pulsed magnetrons and thus
is of importance here.

Mode-skipping is dependent not
only on the characteristics of the
magnetron but also on the charac¬
teristics of the pulser. In practice,
it has been necessary to consider the
magnetron and pulser as a unit.

For given magnetic field and r-f
loading, there is only a limited range
of anode voltage over which the
magnetron will build up oscillations
in the, desired mode. On the other
hand, if high-power oscillations are
to be maintained, a plate voltage at
least as high as this starting voltage
(Fs) must be maintained at large currents. This calls either for a very low-
impedance pulser or for a high pulser voltage To at zero load current.
Consider the case illustrated in Fig. 10-25. To achieve the final pulse
current I, the pulser must be adjusted to a value of To considerably higher
than the starting voltage Vs. Under proper conditions, when the pulse
is applied to the magnetron, the V-I curve is that shown dotted in Fig.
10-25. The pulse voltage never rises above the critical value Vc, because,
as it reaches Fs, the magnetron draws current and loads the pulser. If
oscillation fails to start promptly after the pulse voltage has reached V s ,
the voltage continues to rise and may exceed V c before current is drawn.
Then, since the conditions for oscillation no longer exist, the voltage rises
to Fo and oscillations in the desired mode cannot take place. This is
what occurs when a magnetron skips modes. The V-I trace for such an
event is also shown in Fig. 10-25. The condition for oscillation in the
desired mode occurs when the magnetron starts to oscillate and to draw
current in the time interval taken for the pulse voltage to pass from V s

Fio. 10-25.—V-I plot of a magnetron illus¬
trating the problem of mode skipping.

V» = magnetron starting voltage
V e — critical voltage above which oscilla¬
tions will not start
Vo = pulser voltage with no load.

Skc. 10*6]

MAGNETRON CHARACTERISTICS

355

to V c. For this particular case the probability that the magnetron will
start is increased if (1) the magnetron has a short starting time and has a
large voltage interval Vc-Vs and (2) the pulser delivers a slowly increas¬
ing voltage between Fs and V c . The internal impedance of the pulser,
which determines the distance that Vo must be above Vc, also plays an
important role in mode stability, but the optimum impedance depends
on the characteristics of the magnetron and thus cannot be stated in
general. Particular combinations of magnetron and pulser frequently
present situations much more complex than those shown in Fig. 10-25.
As the phenomenon of mode-changing is becoming better understood,
improvements which alleviate the troubles are being incorporated into
both magnetrons and pulsers. The radar designer should become fully
familiar with the requirements that a magnetron places on pulse shape
and pulser impedance. The reader who needs more detailed information
about magnetrons than is given here is referred to Vol. 6 of this series,
Microwave Magnetrons.

THE PULSER

By J. V. Lebacqz and M. G. White

Modern radar equipments are usually based upon the generation of
short pulses of electromagnetic radiation. The cavity magnetron must
generate electromagnetic oscillation of suitable frequency and power, and
the function of the pulser or modulator is to deliver power to the magne¬
tron in a suitable way. Cavity magnetrons have ordinarily been
employed in the generation of microwaves, but a few radar equipments
have been designed around triode oscillators, notably of the lighthouse
type. Although the pulse techniques described here were largely worked
out with the magnetron in mind, the information presented is intended
to be generally applicable to any oscillator or power-consuming load.
The discussion will be limited to methods peculiarly well adapted to pulse
powers in the range of a few kilowatts up to several megawatts, and to
pulse durations in the range from one-tenth to several microseconds.
The primary aim of the balance of this chapter is to give the designer a
feeling for the over-all problem, and to assist him in deciding among the
compromises required to achieve a well-balanced design.

Numerous considerations enter in the design of a radar pulser; of
primary concern are the nature of the load, the output pulse voltage and
current, the pulse duration, and the repetition rate. The operational
problem faced by the complete equipment will impose some specific
requirements on the pulser, with regard to size, weight, supply voltage,
etc.; such requirements may make it necessary to use an otherwise less
desirable design.

356

THE MAGNETRON AND THE PULSER

[Sec. 10-7

It is common practice to begin the design of a pulser around a resist¬
ance load equal to the static resistance of the actual load to be used at its
required operating point. Although final evaluation of the pulser per¬
formance requires consideration of the whole system and particularly of
the oscillator used, much information about pulser behavior can be
obtained by considering a pure resistance load. The following discussion
of the types of pulsers in use at present and their characteristics is based
on the assumption of a resistance load. The general characteristics of
the magnetron load will be considered later, and their effect on pulser
behavior and design will be studied in greater detail for the two main
types of pulsers.

10-7. Pulser Circuits. -To obtain substantially rectangular pulses
of short duration and high pulse power requires that energy stored in
some circuit element be released quickly upon demand and be replenished
from an external source during the interpulse interval. Either electro¬
static or electromagnetic means of energy storage can be used.

In the latter case, energy stored in the magnetic field of an inductance
through which current is flowing is released to the load by suddenly inter¬
rupting the current. This can be achieved by biasing to cutoff a high-
vacuum tube in series with the inductance, the resulting inductive voltage
rise being applied to the load. To restore the energy to the magnetic
field, it is necessary either to pass large steady currents through the
inductance between pulses, or to use a fairly complicated grid-modulating
circuit whose function is to start the current flowing through the induct¬
ance a short time before the moment of interruption.

In either case, power losses in the switch and auxiliary equipment are
much larger than those in pulsers of comparable output using electro¬
static storage of energy. As a result, the use of pulsers employing elec¬
tromagnetic energy storage has been limited to special applications (such
as trigger circuits) where it is necessary to obtain a very high ratio
between the pulse voltage and the supply voltage or where the load is
mostly capacitive. The following discussions in this chapter will refer
to pulsers whose energy is stored in an electrostatic field.

The basic circuit of most practical pulsers so far designed is given in
Fig. 10-26. Assume for the present that the energy-storage element is a
condenser, Co, charged to a potential Vc so that the energy stored is
^ CoF?- When the switch S is closed at t = 0, the condenser will begin
discharging exponentially through the load resistance R L . If the switch S
can now be opened suddenly at a time t 0 very small compared to the time
constant R L C o of the circuit, the voltage appearing across the load, for
0 < t < U, will be given by

r ‘-M 1 -ffk)

Sec. 10 - 7 ]

PULSER CIRCUITS

357

and will be constant within a few per cent, from the assumption to « R lCY
The voltage left on the condenser is

Hence, the energy dissipated in the circuit during the pulse is

In practice, the only available switches that can be used to open sud¬
denly the large load currents are vacuum tubes—either triodes or tetrodes.

V c

Isolating

element

Energy storing
element

_ .

1 —

’

V L

Supply

L J

/Switch S <•

Fig. 10-26.—Basic circuit for puisers using electrostatic energy storage.

Unfortunately, the plate resistance R p of vacuum tubes is always rather
large, resulting in a high voltage drop V T across the switch during the
pulse. The load voltage will then be given by

Vl = (Vc - V T )

1 -

= Vc

(R P + f?t)CoJ
t

1 -

(Rp + Rl) L (Rp + Rc)C oj

The energy dissipated during the pulse is again given approximately
by

Rp + R ,

- to-

It must be supplied to the condenser during the interpulse interval
through the isolating element. This element thus plays two very impor¬
tant functions in the pulser operation: it must prevent excessive power
being drawn from the power supply when the switch is closed, and it must
allow sufficient energy to flow during the interpulse interval to recharge
the condenser Co- Either a high resistance, an inductance, or a series
combination of resistance and inductance can be used for the purpose.

In order to avoid the large voltage drop across the high-vacuum tube,
it would be desirable to use a very low-resistance switch, such as a spark

358

THE MAGNETRON AND THE PURSER

[Sec. 107

or gaseous discharge, in this circuit. When this is done, however, another
difficulty presents itself immediately: the current flow through a gaseous
discharge switch cannot he interrupted at will, so that all the energy
stored must be dissipated in the load. If the energy-storage element is
still a condenser, then its capacity Co could be made of such a magnitude

that -j CoV% is equal to the required
energy for the pulse, (V\/Rl) to-
This is unsatisfactory, since the
wave shape of the output voltage
pulse would be an exponential,
instead of being substantially rec¬
tangular, as desired.

A satisfactory wave shape can
be obtained with a gaseous dis¬
charge switch if a transmission
line, either parallel wires or co¬
axial cable, is used instead of the
condenser. Consider an ideal
(lossless) line of impedance
Zo = VLjc, where L and C are
the inductance and capacity per
unit length, having a one-way
transmission time S. Elementary
transmission-line theory shows
that if such a line, charged to a
potential Vc, is suddenly con-

Fig. 10-27. —Output of an ideal transmission
line with a resistance load.

nected across a resistance Rl,
there will result a discontinuous

current of magnitude ^— c g- flowing through the circuit for a time
Zo ~r tih

to = 25 , and the voltage appearing across the load (neglecting the small

voltage drop across the switch) will be given by Vl — Vc ^ ft L '

Successive reflections will occur, the amplitude of the nth reflection being
given by

Vl.

= Vc

Zo + Rl

( Rl - Zc Y
\Rl + Zo)

The general wave shape obtained is shown in Fig. 10-27 for three values
of Rl/Zo. Of course, if Rl = Zo, no reflections occur, and a perfect
rectangular pulse is obtained. Even if perfect “match” (Rl = Z 0 )
between the load and the network is not realized, little trouble will
usually occur. Assuming, for example, Rl/Zo = 1.15, the voltage ampli-

Sec. 10-7]

PULSER CIRCUITS

359

tude of the first reflection would be only 7 per cent of that of the main
pulse, and the power involved in that reflection is only 0.5 per cent of that
of the main pulse. For all practical designs, a mismatch of 20 to 30 per
cent is acceptable from the standpoint of energy loss. Design considera¬
tions for the best use of available components usually make it preferable
to keep the impedance Z 0 small, generally about 50 ohms. The load
resistances encountered in practice are approximately 500 ohms or higher.
In such a case, the load and the line are matched through a pulse trans¬
former. The voltage step-up ratio of the pulse transformer, n, is chosen
to make n 2 = Rl/Z o.

If Rl — Z o, it can be shown easily that all the energy stored in the
transmission line is dissipated in the load. Again, from elementary
theory,

z a = VlTc = Vu/cl]

5 = iVlc = VuCo,

where l is the length of the line, L and C its inductance and capacity per
unit length, L 0 = IL the total inductance of the line, and Co = 1C its total
capacity. The energy stored is given by

but

and

W = i C 0 Vl

since to = 25,

W =

to VI
4Z 0 '

On the other hand, the energy dissipated in the load is given by

or, since

V 2

= ¥ to,

Hr,

v L

and

II,

4Z 0 °

Rl — Z o,
W;

therefore all the energy stored in the line is dissipated in the load.

This method thus provides a very efficient way of obtaining a rectan¬
gular pulse of energy in a resistance load. It is usually impractical to use
actual transmission lines or cables in actual pulsers; a cable to supply a
1-gsec pulse would be approximately 500 ft long. This difficulty can be
easily circumvented by the use of artificial transmission lines or of a pulse-
fdrming network.

360

THE MAGNETRON AND THE PURSER

[Sec. 10-7

Now that a practical and highly efficient discharging circuit has been
shown to be feasible, there remains the problem of replenishing the energy
of the pulse-forming network. This could be done by using a resistance
as isolating element. The very low efficiency of this scheme 1 makes it
unsuitable for all but a very few special applications, such as systems
requiring variable interpulse intervals. Accordingly, inductance charging
is almost always used. It will be shown later that, if a d-c supply
voltage is available, the network voltage at the time of discharge is double
the supply voltage, except for losses in the inductance; it will also be
shown that the network can be recharged from a source of a-c voltage,
provided the repetition frequency is a multiple of one-half the supply
frequency.

Comparison of the Two Types of Pulsers .—The basic circuit of Fig.
10-26 applies, as has been shown, to two types of pulse generators. In
one type a small amount of the energy stored in a condenser is allowed to
be dissipated in the load during each pulse. The switch, which must be
able to interrupt the pulse current, is always a vacuum tube, and pulsers
of this type are commonly called “hard-tube pulsers.” Pulsers of the
other type, where exactly the correct amount of energy is stored before
the switch is closed, and the pulse is shaped by the discharge circuit itself,
are referred to as “line-type pulsers,” since the pulse-shaping elements or
pulse-forming networks have been derived from the electrical characteris¬
tics of transmission lines.

The two types of pulsers have different characteristics, and it is of
interest to analyze briefly some of the considerations involved in the
design.

For instance, it is easier to change the pulse duration in a hard-tube
than in a line-type pulser, since it is sufficient to change the time during
which the switch is conducting. This can be done easily at low voltage
in the driver stage, instead of using a high-voltage switch to change pulse¬
forming networks in a line-type pulser.

Methods for turning on the switch in a hard-tube pulser, discussed
more fully later, generally involve a small regenerative pulser which
applies a positive pulse “drive” to the control grid of the vacuum-tube
switch. This small pulser nearly always requires auxiliary voltage sup¬
plies and, in addition, the switch-tube control grid must be maintained
beyond cutoff during the interpulse interval. In line-type pulsers, the
“triggering” of the switch (or initiation of the discharge) is usually
accomplished with much less power than is necessary to drive the grid
of the hard tube; in most cases, the driver power output is only a few per

1 Simple considerations show that, when charging a condenser from zero to the
power supply voltage through a resistance, as much energy is dissipated in the resist¬
ance as is stored in the condenser.

Sec. 10-7]

PULSER CIRCUITS

361

cent of the pulser power output, but it runs as high as 10 per cent in some
high-power pulsers. The output pulse shape is usually more nearly
rectangular from a hard-tube than from a line-type pulser. Except for
special cases, hard-tube pulsers are almost always built for direct output,
and thus avoid the inductance and capacity added by the impedance¬
matching pulse transformer between the line-type pulser and the load,
with the resulting oscillations in the
pulse shape.

Power regulation as a function
of input voltage, that is, the ratio
of the fractional increase in output
power to the fractional increase in
input voltage which produces it, is
always equal to 2 for a line-type
pulser operating near matched con¬
ditions, regardless of the type of
load. For a hard-tube pulser op¬
erating a load having the general
characteristics of a biased diode—
such as the magnetron—the regula¬
tion may be as high as 5 or 6 if the
pulser is designed to operate with
minimum tube drop. It is possible,
however, by choice of switch tubes with proper characteristics, to operate
on such a portion of their characteristic that the power regulation near the
operating point will be only about 0.5.

The pulser load line, or variation in output voltage and current as a
function of load, is a plot of load voltage vs. load current (see Fig. 10-28).
An equation for the line-type pulser is easily obtained, by eliminating R L
between the expressions for load current and voltage, as Ft = V c — IlZ 0 .
It is thus a straight line. For hard-tube pulsers, the same expression is
applicable if Z 0 is replaced by the tube resistance R p . In this case, how¬
ever, R p is not a constant, but depends on the tube characteristics.

When variable pulse spacing, very high pulse repetition rates (greater
than 4000 pps), or “coded pulses” (groups of closely spaced pulses) are
required, the hard-tube pulser is almost exclusively used. Although the
line-type circuit can be adapted to such an application, 1 the advantages
of flexibility inherent in the hard-tube pulser have restricted the use of
the line-type pulser to very special cases. Such a case occurs if the supply
voltage is so low that the required power output cannot be obtained from
a hard tube.

“Time jitter,” or the difference between the time at which a pulse is

1 See Sec. 10-7, Vol. 5, Radiation Laboratory Series.

Flo. 10-28.-—Pulser and magnetron
voltage-current characteristics, (a) line-
type pulser load line, ( b ) hard-tube pulser
(adequate emission available), (c) hard-
tube pulser near saturation.

362

THE MAGNETRON AND THE PULSER

[Sue. 10-8

supposed to appear and that at which it does appear, is sometimes a very
important factor to be considered in the design of the pulser (Chap. 16).
For hard-tube pulsers, the time jitter is practically always of the order
of 0.01 Msec or less. Some specially designed gaseous discharge switches
(hydrogen thyratrons and mercury-sponge series gaps) can also give time
jitters of the same order of magnitude, if the proper precautions are taken
in the trigger circuit. Others have time jitters ranging from ^ to 3 Msec
for cylindrical series gaps, to 20 to 50 Msec for rotary gaps.

The simplest type of pulser is one of the line type, with a-c charging
and a rotary-gap switch. In this case, the pulser components are
reduced to a pulse-forming network, a charging transformer (which com¬
bines the functions of input step-up transformer and charging inductance),
and a rotary gap mounted on the shaft of the alternator which supplies
power to the charging transformer. In this way, the proper relationship
between supply and repetition frequencies is easily maintained, and a very
compact pulser for high power output can be made, although such a pulser
has no flexibility.

In general, line-type pulser circuits are simpler and therefore easier to
service. They also lend themselves to a greater efficiency, not only
because the circuit in itself is more efficient, but because the overhead—
auxiliary circuits, cathode power, etc.—is less. In size and weight, for a
given set of output conditions, the advantage is decidedly with the line-
type pulser. For airborne pulsers, these advantages in efficiency, size,
and weight outweigh any advantage of flexibility or pulse shape which
the hard-tube pulser may offer. As an example, the Model 3 airborne
pulser (used in the AN/APS-15), rated at 144 kw pulse power output
with pulse lengths of 0.5, 1, and 2 m sec, weighs 55 lb and occupies a space
15 by 15 by 16 in.; with the techniques now available little improvement
could be expected, were this pulser redesigned. On the other hand, a
line-type pulser with hydrogen-thyratron switch, designed for 600 kw
pulse output, for pulse widths of 0.5 and 2.5 nsec, weighs only 98 lb and
has a volume of about 17 by 17 by 24 in.

Table 10 3 summarizes the advantages and disadvantages of the two
types of pulsers.

10-8. Load Requirements. —It is not enough to say that a pulser
shall produce a pulse of a certain duration and magnitude. The nature
of the load imposed upon the pulser, the operational problem faced by
the complete equipment, and certain other practical factors usually
require consideration.

Although the most usual pulser load is the magnetron, the load prob¬
lem in general will be considered briefly. The eventual load will differ
from a pure resistance by having a certain amount of capacity and induct¬
ance associated with it, and it will certainly be nonlinear. Further, the

Sec. 10-8]

LOAD REQUIREMENTS

363

Table 10-3.— Comparison of the Two Pulser Ttpes

Characteristics

Hard-tube pulser

Line-type pulser

Efficiency

Lower; more overhead power
required for driver, cathode
heating, and for dissipation
in switch tube

High, particularly when pulse-
power output is high

Pulse shape

Better rectangular pulses

Poorer rectangular pulse, par¬
ticularly through pulse trans¬
former

Impedance-matching

Wide range of mismatch per¬
missible

Smaller range of mismatch per¬
missible ( ± 20-30 per cent).
Pulse transformer will match
any load, but power input to
nonlinear load cannot be
varied over a wide range

Interpulse interval

May be very short, as for cod¬
ing beacons (i.e., < 1 /xsec)

Must be several times the
deionization time of discharge
tube (i.e., > 100 jisec)

Voltage supply

High-voltage supply usually
necessary

Low-voltage supply, particu¬
larly with inductance charg¬
ing

Change of pulse dura-

Easy; switching in low-voltage

Requires high-voltage switch-

tion

circuit

ing of network

Time jitter

Somewhat easier to obtain
negligible time jitter, i.e.,
< 0.02 ,'sec, than with line-
type pulser

High-power line-type pulsers
with rotary-gap switch have
inherently large time jitter.
With care in design and use
of hydrogen thyratron or
mercury-sponge type of en¬
closed gaps, time jitter of
0.02 jisec or less obtainable

Circuit complexity

Greater, leading to greater
difficulty in servicing

Less, permitting smaller size
and weight

Effects of change in

For design having maximum

Better than a hard-tube pulser

voltage

efficiency, (AP/P) output «
6(AV/'V) input. By sacri¬
ficing efficiency in the design,
(AP/P) output ~ 0 5 (AV/V)
input can be obtained

designed for maximum effi¬
ciency since (AP/P) output
« 2(AV/V) input for line-
type pulser, independent of
design

load may also display occasional short-circuit and open-circuit conditions
which must be allowed for in the pulser design.

Confining our attention to the magnetron, we note in Fig. 10-29 that
it displays a dynamic impedance at the operating point of only 430 ohms,
even though the V-I impedance ratio is 1480 ohms there. Both the
operating and the dynamic or incremental impedance are important ; the
former determines the rate at which power will be absorbed from the

364

THE MAGNETRON AND THE PULSER

[Sec. 10-8

pulser, and the latter determines in some cases the variation in power
output with small incremental changes in applied voltage. For example,
a magnetron operating at 20 kv and 13.5 amp absorbs power at the rate
of 270 kw, yet a decrease in applied voltage of only 3 kv will drop the
current by 7 amp and virtually stop the oscillation. Since AV/Al is
small, a satisfactory pulser must produce a fairly flat-topped pulse free
from voltage changes larger than 5 per cent of the peak voltage.

The V-I characteristics of most magnetrons show irregularities which
are associated with various modes of oscillation whose number, magni¬
tude, and position vary with magnetron type, r-f load applied to the

magnetron, magnetic field, and
cathode condition.

Short-circuit and open-circuit
conditions must be allowed for if
the pulser is not to be damaged. A
magnetron, or any other load, may
develop an infinite impedance be¬
cause of mechanical breakage of
some part of the circuit, or through
failure of the cathode to emit. This
is not serious in the case of the hard-
tube pulser, but the pulse-forming
network variety generally dis¬
charges its unconsumed energy in
some abnormal and undesirable
way. No pulsing system should be
considered which can be destroyed
by a single discharge of a high-power
Peak plate current in amperes pulse in some unexpected part of the

Fig. 10-29. V-I characteristics of 4J77 mag- circuit. An average-current device
netron. Field, 2700 gauss; X = 11.140 cm. . . .

intended to turn on the primary
power supply if the load fails to draw power could hardly do so in less than
a few pulse cycles, and thus cannot be relied upon to protect against this.

A short-circuited load can prove disastrous to a hard-tube pulser in a
few pulse cycles unless provision is made to turn off the primary power
when the load draws too much current, since most of the energy which
the hard-tube pulser normally delivers to the load will then appear as
anode heating of the switch tube. Since it is hardly practicable to design
switching tubes heavy enough to withstand this sort of abuse for long,
overload protection must be provided. A relatively fast-acting average-
current device is suitable for this purpose.

The electrostatic capacity of the load should nearly always be kept
to a minimum. Not only is the energy spent in charging this capacity

Sec. 10-8]

LOAD REQUIREMENTS

365

totally wasted, but stray load capacity seriously affects time of fall and
back-swing. Short, well-spaced leads and a low-capacity magnetron fila¬
ment transformer are helpful in reducing load capacity.

The definition of pulse duration is intimately bound up with mag¬
netron behavior. From the radar system point of view it is the duration
of the r-f pulse which is of interest and not necessarily the duration of the
voltage pulse applied to the magnetron. Figure 10-30 shows the typical
appearance of the r-f pulse, of the current pulse through the magnetron,
and of the voltage pulse applied to the magnetron. Usually, the shape

Fia. 10-30.—Time variation of voltage and current of a pulsed cavity magnetron.

T r = time of rise of voltage wave
T a — delay time for onset of oscillations
to = width of current and r-f pulse
Tf = time of fall of voltage wave.

and duration of the r-f pulse closely approximate those of the current
pulse; the voitage pulse is less steep and of longer duration.

The pulse length, to, may be defined as the interval of time during
which the load current wave is within 50 per cent of peak value. In so
defining the pulse length, it is necessary to ignore a rather short-duration,
high-current spike often found on the leading edge of the current wave.
So defined, to can be used satisfactorily in calculations of average current
and average r-f power. Successful pulsers have been designed and put
into production for to as short as 0.1 nsec, and as long as 5 usee or a little
more. Practical design difficulties increase at pulse lengths outside this
range.

The voltage across the magnetron when it is oscillating vigorously in a
steady state is designated as F m o. In general, F m0 will lie between a few
kilovolts and 30 to 40 kv, although it may be higher for magnetrons in the
10-Mw region. Most practical pulsers do not produce a perfectly uni¬
form flat-top wave because this is usually costly and unrewarding. A
drop of 2 to 5 per cent in voltage during the pulse, AF m0 , can usually be
tolerated by the magnetron without harmful frequency modulation or
mode instability.

366

THE MAGNETRON AND THE PULSER

[Sec. 10 8

The rate of rise and the overshoot on the leading edge of the voltage
wave are important in determining the ability of the magnetron to
operate at high power levels. A multicavity oscillator has several possi¬
ble modes of oscillation, in only one of which it operates efficiently and
smoothly. Great effort has been devoted to understanding the conditions
favorable to stable oscillations in a given mode. We now know that
stability depends on both pulser and magnetron. Usually the pulser
can be more easily modified than the magnetron if mode-shifting or mode¬
jumping occurs. In any event, many interacting adjustments must be
made before full power output can be assured. Sometimes a change in
the r-f loading of the magnetron, in its heater current, or in the shape of
the magnetic field will succeed where altering the pulse shape has failed.
Almost always, too short a rise time, t T , of the voltage pulse leads to mode
instability, any rate of rise over 100 kv/gsec being considered fast. 1
Magnetron sparking can also be caused by high rates of voltage rise.

A “spike” frequently appears on the leading edge of the voltage pulse.
Since a magnetron operates at a magnetic field far above the nominal
cutoff value, it is impossible for electrons to reach the anode without the
aid of the r-f field. Therefore, until the field is established, little power
is drawn from the pulser and a momentary overvolting of the magne¬
tron results. This phenomenon is particularly prominent in the case of
line-type pulsers, where the voltage across the magnetron can rise to
twice normal if the magnetron fails to draw power. This high-voltage
“spike” can give rise to all manner of sparking and mode troubles. Its
cure lies not alone in alteration of the pulser design, but also in attention to
magnetron design. 2

The internal impedance of the pulser plays an important role in affect¬
ing mode stability. There are significant differences between the opera¬
tion of hard-tube and of line-type pulsers. 3 The hard-tube pulser has an
internal impedance equal to that of the output tube, which varies from
90 to 150 ohms until saturation is reached. The line-type pulser, being
essentially a constant-voltage device in series with an impedance equal
to the load resistance, has a resistance of 400 to 1200 ohms. Conse¬
quently, the conditions of stable operation for a given magnetron will
vary with load and pulser type. Stable operation occurs for those
values of V and I which simultaneously satisfy the load and generator
characteristics. This would not concern us except that the various
modes have different V-I characteristics, thus giving cause for instability.

1 The 4J52 magnetron is an exception to the statement made here, br ing more
stable with a rapid rate of rise.

2 More detailed discussions will be found in Pulse Generators, Vol. 5 of this series,
and in Microwave Magnetrons, Vol. 6.

3 RL Report No. 809, Sept. 28, 1945.

Sec. 10 9]

THE HARD-TUBE PULSER

3G7

Figure 1028 shows how differing internal impedances can affect mode
stability: operation in the unwanted fjr mode is impossible in the case of a
pulser load line such as B, but may occur if the load line has the form of
A or C.

We must also pay attention to the reverse voltage V m i which most
pulsers put across the magnetron after the main-power pulse has passed,
for in some cases V ml may be larger than V m o and lead to breakdown of
the magnetron insulation. This same reverse voltage may also appear
across various parts of the pulser circuit itself unless steps are taken to
suppress it. Most pulsers keep the reverse voltage within safe limits by
means of a resistance or, better still, a nonlinear element such as a diode.
The power wasted in backswing damping is rarely more than a few per
cent of the total useful power output of the pulser, and the duration of
the backswing is seldom greater than 2 to 10 gsec. Some pulsing circuits
produce a secondary forward pulse, V„ 2 , which can cause trouble by
feebly exciting the magnetron to give a few microwatts of power. In

C 0

E s E„=*\3 Vm
1200 v

Fig. 10-31.—Schematic diagram of output
stage of hard-tube pulser.

many applications this would cause
no concern because of the much
greater amplitude of the main power
pulse. In most radar systems,
however, a few microwatts, directly
from the magnetron, would swamp
any but the strongest echoes which
might happen to return coinciden¬
tally with the appearance of y m2 .

As a matter of practical experience,

V m 2 should be kept below 10 per
cent of V m0 if all possibility of
trouble is to be avoided.

10-9. The Hard-tube Pulser. —A simplified diagram of the power-
output stage of the hard-tube pulser is given in Fig. 10-31. The energy-
storage element Co is recharged through the isolation inductance L i. In
the quiescent state, the point A' is at ground potential while the high-
voltage side of Co is at the full d-c supply voltage along with the anode of
vacuum tube T\. The control grid of T i is biased to cutoff and the screen
grid is held at a normal positive value. If a sufficiently large positive
pulse be applied to the control grid of T i, the cathode will emit electrons
vigorously and the anode will drop from its high positive potential to just
that potential required to pass the plate current demanded by the load.
Since the voltage across Co cannot change instantaneously, the point A'
will assume a high negative voltage, which is applied to the load. Cur-
rert will continue to flow out of Co, and around the load circuit, until the
driving pulse on the grid of T i is removed. The system will return to its

368

THE MAGNETRON AND THE PULSER

[Sec. 10-9

previously described quiescent state as soon as current can flow through
L 2 R 2 to bring the point A' back to ground, and as soon as recharging cur¬
rent can flow slowly through L\ to return C 0 to its fully charged condition.
During the pulse, the potential of C 0 (and hence the voltage across the
load) slowly declines unless Co is made very large. In any practical
design it is usually desirable to make C 0 no bigger than absolutely neces¬
sary, the criterion being the permissible voltage drop while carrying
a current pulse of definite magnitude for the duration of one pulse.
Expressed more quantitatively, C 0 = Ito/AV m0 . If I = 10 amp, i 0 = 1
psec, and the permissible voltage drop AF m o = 100 volts, we find that C 0
must be 0.1 gf. The sizes of L 1 , Li, and R 2 depend upon how quickly it is
desired to bring the tail of the pulse down to zero once the grid drive has
been removed, and also on how much energy one is willing to waste in
these elements during the pulse.

There exists an upper limit to the size of the coupling condenser,
because a very large capacity would take longer to recharge fully after a
pulse. Given a fixed pulse rate and recharging impedance, an increase
in coupling capacity will be accompanied by an increase in the no-load
to full-load voltage ratio. In effect, a large capacity gives poor regula¬
tion. Should the designer attempt to recover this loss by decreasing the
size of the recharging impedance, there will result an increased current
drain from the power supply through the switch tube during the pulse,
thereby causing an increased switch-tube drop. Careful balancing of
these factors is required to achieve most efficient design.

Occasionally, the most efficient operating voltage of the magnetron
or load does not correspond to the optimum plate voltage for T 1( so that
there must be some impedance-matching device between pulser and load.
The primary of a pulse transformer may be inserted at A A' and the load
connected across the secondary with or without the damping element
L 2 R 2 . Generally speaking, the insertion of a pulse transformer changes
so much the character of the pulse tail that it is necessary to alter radically
the so-called “tail damping” circuit. The most flexible and satisfactory
damping system is a high-voltage diode connected across the magnetron
to draw power only on the backswing.

The Switch Tube .—Since the vacuum-tube switch is the heart of the
hard-tube pulser, the characteristics desirable in a switch tube will be
briefly mentioned. It must be able to carry easily the current demanded
by the load; in the interest of efficiency, the anode potential required
should be as low as possible. Since a major source of power waste in the
circuit is in the cathode-heating required to sustain the desired emission,
it is customary to use oxide-cathode emitters wherever possible. Unfor¬
tunately, oxide-cathode tubes are not easily adaptable to high anode
voltages because of the phenomenon of cathode sparking. With proper

Sec. 10-9J

THE HARD-TUBE PULSER

369

care in processing and use it is possible, nevertheless, to arrive at a satis¬
factory and highly flexible pulser design using the oxide-cathode pulse
tube up to 20 kv. Where extreme reliability and relative immunity to
overload are required, the designer will prefer the thoriated-tungsten
cathode switch tube in spite of its greater cathode power requirements.
Switching tubes of the oxide-cathode variety usually can be counted upon
to emit 300 to 600 ma/watt of heating power while the emission of the
best thoriated-tungsten cathodes is only about 100 ma/watt.

The oxide-cathode tube is limited in power output by the onset of
grid emission. It is impossible to prevent thermionically active cathode
material from contaminating the grid structure. Great care must be
taken, therefore, to cool the grid by fins, heavy rods, and other means, for
it can emit a few milliamperes even at a sub-visible temperature. A few
milliamperes may sound small in comparison with several amperes pulse
current, but a few milliamperes flowing all the time can cause serious
heating of the anode and screen, which are at relatively high potentials.
Usually the result is a runaway condition in which grid control is lost.
The most successful oxide-cathode high-power switch tube is the 715B
developed at Bell Telephone Laboratories. The 715B has a gold-clad
grid which poisons and “absorbs” active material, thereby lowering its
efficiency as a thermionic emitter.

Table 10-4.— Typical Operating Characteristics

Tube

type

Cath¬

ode

type

Cath¬

ode

power,

watts

Max.
plate
volt¬
age, kv

Pulse

cur¬

rent,

amp

Emis¬

sion,

amp/

watt

Cutoff

grid

volt-

age*

Plate

drop,

volts

Screen

volt¬

age

Positive

grid

drive,

volts

3D21

Oxide

3.5

0.5

- 70

400

800

150

3E29

Oxide

5.0

0.57

- 1001

600

800

150

715B

Oxide

15.0

0.27

- 500

1500

1200

200

5D21

Oxide

20.0

0.27

- 500

1500

1200

200

304TH

Th-W

125

15.0

0.05

- 900

2000

200

6C21

Th-W

140

30.0

0.11

-1000

1500

6D21

Th-W

150

37.5

0.10

- 500

2000

1500

527

Th-W

770

30.0

0.08

-1200

1500

* 0.2-ma cutoff.

A good output pulse tube must possess a sharp grid cutoff. For
efficient operation, the plate current must be one milliampere or less when
the grid is biased to some reasonable value. Because the anode is at very
high voltage between pulses, any “leakage current” delivers excessive
power to the anode. As an example, consider a pulse tube normally
giving 20-amp pulses with an anode drop of 3 kv at a duty ratio of two-
Such a tube will display a peak power anode loss of 60 kw, but an average
power loss of only 60 watts. If the leakage current at “cutoff” amounts

370 THE MAGNETRON AND THE PURSER [Sec. 10-9

Sec 10-9]

THE HARD-TUBE PULSER

371

to only 1/10,000 of the peak current, or 2 ma, the power loss at 35 kv
anode voltage is 70 watts. To reduce leakage current, the grid structure
of a switch tube must surround the emitting area of the cathode com¬
pletely, and must give a uniform field over the entire cathode. Figure
10-32 shows a group of high-vacuum switch tubes; Table 10-4 gives a set
of typical operating characteristics.

Except for the screen-grid and control-grid bias requirements of power
output and driver stages, the hard-tube pulser is rather simple, for (as is
shown in Fig. 10-33) the grid-driving circuit is not inherently complicated.
A single 829 or 3E29 tube at Ti will satisfactorily drive two Eimac
304TH’s or two Western Electric 715B tubes; either complement of tubes
is adequate to deliver over 200 kw to the load. Circuit constants given
in Figs. 10-31 and 10-33 are representative and have been used in a pulser
produced in large quanties. With the constants shown, the output volt¬
age pulse has a nominal duration of 1 gsec at 12 kv and 12 amp. The
maximum duty-ratio limit, set by
the 715B tube, is 1/1000.

If higher powers are required,
it is quite practical to use several
715B’s in parallel. High-voltage
tubes such as the 6C21 can be op¬
erated either singly or in parallel.

In the case of parallel operation,
it is sometimes necessary to insert
25 to 50 ohms into the plate and
screen leads in order to prevent
parasitic oscillations.

The Driver Circuit .—In the
grid-driving circuit of a hard-tube
pulser, all the requirements for
pulse shape, accuracy of pulse spacing, and flexibility of pulse rates must be
met. The important parts of the regenerative pulser circuit shown in Fig.
10-33 are the pulse-forming network at the left and the three-winding pulse
transformer which provides the necessary plate-grid feedback to make the
circuit self-driving.

Normally, all tubes are biased to cutoff; therefore, when a positive
pulse of 100 volts is applied to the “trigger in” point (Fig, 10 33), plate
current starts to flow in 7/, inducing a further positive voltage on the
grid of 7V Once regenerative action has commenced, the input trigger
has no further effect; the plate current increases rapidly until limited by
the e p -i p characteristic of T 2 . As i p increases, e p decreases until it nears
the screen potential; from there on, i p increases only slowly, thus pro
ducing a relatively flat-topped wave.

Transformer ratio

Fig. 10 33.—Schematic diagram of regen¬
erative pulse generator used as driver of hard-
tube pulser.

Fig. 10*34.— High-power hard-tube pulser.

THE MAGNETRON AND THE PULSER [Sec. 10-9

Sec, 10-9]

LINE-TYPE PULSERS

373

During the rising part of the plate current curve, the pulse trans¬
former induces a negative voltage wave on the delay line equal to the
induced positive voltage on the grid. The pulse length is then fixed by
the time required for this negative wave to travel down the line and back
to the grid. Upon arrival at the grid, the negative wave drives the tube
toward cutoff, a process helped again by the regenerative action of the
pulse transformer.

Fig. 10-35. —Hard-tube airborne pulser.

Practical Considerations .—The most economical pulser would have
power flowing only during the pulse. Of course, energy must flow back
to recharge those elements which store and deliver pulse power, but the
design should not include vacuum tubes that conduct during the time
between pulses, and are turned off during the pulse. Judicious use of
plate-coupled and cathode-coupled circuits usually will permit all tubes
to be biased to cutoff except during the pulse. Pulse transformers can
also be used for phase reversal, impedance-matching, and circuit isola¬
tion. Means are now available for computing the important design
parameters of such pulse transformers. 1

Successful hard-tube pulsers have been made with power outputs up

1 Pulse Generators, Vof. 5, Chaps. 12 to 15, Radiation Laboratory Series.

374

THE MAGNETRON AND THE PULSER

[Sec. 10-10

to 3 or 4 Mw by operating half a dozen high-voltage 6D21 thoriated-
eathode tetrodes in parallel. Figure 10-34 shows two views of a high-
power hard-tube pulser rated at 3 Mw and Fig. 10-35 shows a lightweight
hard-tube pulser built for airborne use. The latter is rated at 144 kw
output at pulse durations of 0.5, 1, and 2 nsec; it employs a circuit veri¬
similar to one given by combining Figs. 10-31 and 10-33.

10-10. Line-type Pulsers.- —A schematic diagram applicable to most
typical line type pulsers is shown in Fig. 10-36. Like the hard-tube
pulser, the line-type pulser is best analyzed by separate consideration of

Fio. 10-36.—Basic circuit for a line-type pulser. Voltajo may be either d-c or some periodic
function of the time, such as V = V„ sin 27rft.

the discharging and the recharging circuit. The discharging circuit is
very simple, and its individual components are discussed in some detail
hereafter. The pulse transformer will be considered in the following sec¬
tion, since it is applicable to both types of pulsers. In general, it can be
said that the effect of both the switch and the pulse transformer is to
decrease the rate of rise of voltage at the load from that which would be
produced by the network alone. The switch usually introduces an
appreciable resistance during its ionizing time, and the pulse transformer
introduces an additional inductance in series with the load. However, a
spike voltage is often encountered in practice, as mentioned previously,
because of the time required for the magnetron to draw current after
the normal voltage is applied to it. When it is necessary to prevent the
appearance of a spike, a “despiking” circuit is used as indicated in the
diagram. The resistance of this circuit is chosen equal to the network

Sec. 1010]

LINE-TYPE PULSERS

375

impedance, and the capacity is chosen small enough to be almost com¬
pletely charged a very short time after the oscillator draws full load cur¬
rent. A damping network may also be provided to help bring down the
trailing edge of the voltage pulse and prevent post-pulse oscillations.

The Pulse-forming Network .—One of the possible lumped-constant
networks having electrical properties essentially equal to those of a
transmission line is given in Fig. 10 37, with the values of L and C neces¬
sary for a line of given impedance and pulse length. If the inductance is
constructed by winding a uniform helix on an insulating cylinder, the
ratio of coil length to coil diameter should be that shown in Fig. 10-37, in
order to provide the right amount of coupling between coils. The appro¬
priate value of inductance at each end of the line differs slightly from that
in the middle sections. It has been found practically that the optimum
number of meshes is related to the desired pulse length as shown in the
following table.

Table 10 5. —Relation ok Pui.se Length to Number of Meshes
Pulse length, nsec Number of meshes
0.1-0.5 1-3

0.5-2.5 2-5

2.5-5 3-8

The greatest obstacle to design of a compact high-power network is
the bulk of the necessary condensers. High-voltage condensers are

inordinately large and expensive
in comparison with the job they
have to perform; all electronic
equipment would profit from a
major improvement in condenser
design. Though a few new di¬
electrics have shown promise of
increasing the energy stored per
unit volume, mica, paper, and oil
are still the primary dielectrics for
high-voltage condensers. One
new material of interest is Alsifilm

Diameter

Fig. 10-37.—Type E pulse-forming network.

to = 2 n \/LqC

l_ = 4
d 3
L

-- = 1.1 to 1.2
L o

or Diaplex, an aluminum-silicate
clay in an organic impregnate.
This material can be formed into
thin, homogeneous sheets w r hich
have dielectric properties superior
to mica or paper and oil. The

Lo = inductance per mesh
L = end inductance
C = capacity per mesh
n ~ number of meshes
Zo = surge impedance
to = pulse length
l = coil length of one mesh
d = coil diameter.

dielectric constant is 5 to 6 and the safe operating dielectric strength is 500

to 700 volts per thousandth of an inch. Greater uniformity would raise

the latter to 800 volts per thousandth. Most problems of fabrication have

THE MAGNETRON AND THE PULSER

376

[Sec. 10-10

been overcome. Perhaps TiC> 2 , or some similar material of high dielectric
constant, will find wide use outside the low-voltage field.

Another promising approach to the condenser design problem is the
electrochemical formation of very thin insulating films on metal (such
as those employed in the electrolytic condenser) on which a layer of metal
is then deposited. High capacity per unit area results from the very
small spacing, but the insulating film must be able to withstand the
extremely high field strengths thus imposed.

Further attention to the details of mechanical design of condenser
fittings—containers, bushings, connectors, and the like—is also required.
The over-all bulk even of condensers using conventional dielectrics can

still be considerably reduced.
Figure 10 38a shows typical pulse¬
forming networks, the ratings for
which are given in Table 10-6.
Figure 10-386 shows a network
used in an experimental 20-Mw
pulser, the largest designed at
Radiation Laboratory. Two of
the smallest networks used are
shown for size comparison: the one
on the left has a rating of 5 kw
pulse power output; the other one is electrically equivalent to the net¬
work (1) of Fig. 10-38a, but uses r ..

Fig.

10*38a.—Pulse-forming networks
Table 10.6 for properties).

Wlilll 111 mi I IIMN'i M#f IMWMI
iimi uiiii jmiiu mu.

MUNii.MiHiTiumuiriiinfHiii.uiii'rMv.'..

Diaplex insulation.

The network designer has con¬
trol of pulse length and impedance
level independently of one an¬
other. The pulse length is ordi¬
narily fixed by the nature of the
application, while the impedance
level is chosen to fit the character¬
istics of the load, the switching
tube, and the power supply. A
pulse transformer can be inserted
between load and pulse-forming
network so that the network can be designed to use the available switching
device most efficiently. Once the pulse power output is settled and the
appropriate switching tube chosen, Z 0 can be determined from one of the
relations P = P 0 ■ Z 0 or P = V\/Z {) . Usually either I 0 or V 0 is definitely
limited for a given switch; this indicates the appropriate relation to use
in calculating Z 0 . It must be remembered that the voltage across the
pulse network (and hence across the switch) is twice the voltage delivered
to a matched load.

Fig.

10-38&.—Experimental
network.

pulse-forming

Sec. 1010]

LINE-TYPE PULSERS

377

In large radar equipments, it is often desirable to separate pulser and
r-f units by considerable distances. The pulse transmission cable neces¬
sary in such cases has been standardized at an impedance level of 50
ohms. Many pulse networks designed for high-power radar have an
impedance of 50 ohms in order to avoid the use of a matching pulse trans¬
former between the network and the cable. As a result, many of the
more desirable switching devices have been designed to give maximum
power output when used with a 50-ohm network.

Table 10-6.— Pulse-forming Network Characteristics

Network (Fig. 10-38)

Pulse length, pse c

PRF, cps

Power

No. 1

0.8

840

25 kw

2.2

420

25 kw

No. 2

0 25

1600

250 kw

0 5

800

250 kw

2.6

400

250 kw

5 2

200

250 kw

No. 3

1000

250 kw

No. 4

800

3 Mw

An important design consideration in pulse network applications is
the average power to be handled. A pulse network designed to have
adequate life at one pulse rate would overheat and perhaps be ruined by
operation at a higher repetition frequency. Since overheating is a func¬
tion of both applied voltage and repetition rate, little flexibility remains
in a line-type pulser designed to achieve maximum economy of weight,
space, and power. Provision can be made for shortening pulse length
by bringing out taps on the pulse line. However, this is rather difficult
at high power, because of the problem of designing suitable line switches.

The Switch .—The possible advantages of the line-type pulser greatly
stimulated the design of low-impedance spark switches and thyratrons,
since it became possible to secure flat-topped pulses without the necessity
of opening the switch. Rotary spark gaps, “trigatrons,” series gaps,
hydrogen thyratrons, and mercury thyratrons have all been used as net¬
work switching devices. Each has its field of application. Each switch
is limited in one or more of the following respects: (1) poor precision of
firing, (2) low maximum pulse rate, (3) short life on long pulses, (4) nar¬
row operating range of voltage, (5) occasional erratic firing, (6) inefficient
cathode, and (7) unnecessary complication. The ideal switch has not
yet been designed.

Figure 1039 shows schematically the simple “series gap” sw'itch.
The Western Electric 1B22 is a good example of this class of switch; it
consists of a cathode cylinder of aluminum surrounding an anode rod of

378

THE MAGNETRON AND THE PULSER

[Sec. 10-10

the same material. The tube is filled to a pressure of a little less than one
atmosphere with a mixture of 75 per cent hydrogen and 25 per cent argon.
Two or three tubes are used in series, with a voltage divider across them
to ensure that the network voltage is divided equally among all the gaps
before the pulse takes place. Triggering is accomplished as shown in
Fig. 10-39 by depressing or raising quickly the voltage of the two middle
electrodes. This breaks down one of the gaps and throws full voltage
across the second gap. The overvolted second gap thereupon also
breaks down, forming a low-impedance path between points A and A'.
These switches are efficient and are quite satisfactory in use. Their chief
limitations are in the allowable pulse repetition frequency (about 2000

pps maximum) and in obtainable precision of pulse timing. This type

of switch can handle several mega¬
watts, and should be useful in appli¬
cations that do not require great
flexibility or accuracy of firing.

A particularly successful version
of the series-gap switch is the Bell
Telephone Laboratories’ 1B42,
which substitutes a mercury-sat¬
urated iron “sponge” for the solid
aluminum cathode of the 1B22. By

Fig. 10-39.—Series gaps.

Fig. 10 40.—Trigatron.

using an atmosphere of relatively high-pressure hydrogen, the temperature
variation of mercury vapor pressure is made unimportant. Since the
ordinary series gap is limited in operation by pitting and spike growth,
the mercury cathode provides better operation over a wide range of

Sec. 10-10]

LINE-TYPE PULSERS

379

operating conditions as well as longer life at higher frequencies.
Apparently the mercury cathode series gap can be designed to fire very
precisely.

The “trigatron” (Fig. 10-40) differs from the series gap in having
but one spark gap, across which the full line voltage is applied. Conduc¬
tion is initiated by applying a steep high-voltage wave to a trigger elec¬
trode; this presumably draws corona current sufficient to initiate the
main discharge. A typical trigatron is the British CV85. This has three
electrodes in a mixture of argon and oxygen at a pressure of approxi¬
mately 3 atmospheres. A triggering voltage of approximately 4 kv is
required to fire the tube when it is to deliver 125 kw of pulse power into
a 70-ohm load. The precision of triggering usually is about +0.2 gsec,
unless special precautions are taken to insure correct trigger wave shape
and amplitude.

The most versatile switch is the newly developed hydrogen thyratron
(Fig. 10-41), which requires a positive trigger of only 150 volts rising at
the rate of 100 volts per /isec. In
contrast to spark devices, the hy¬
drogen thyratron will operate over a
very wide range of anode voltages
without readjustment. This char¬
acteristic is particularly important
for experimental pulsers, or for any
pulser whose probable load is in
doubt. In general, it is difficult to
reduce the voltage across a spark
switch by more than a factor of 2
from the nominal design voltage
without encountering erratic opera¬
tion. Voltages substantially higher
than the nominal design value cause
a flash-over in the switch. The hy¬
drogen thyratron, on the other
hand, is a true thyratron. Its
grid has complete control of the
initiation of cathode emission over a wide range of anode voltage. The
anode of a hydrogen thyratron is completely shielded from the cathode
by the grid. The effective grid action results in very smooth firing over
a wide range of anode voltages and repetition frequencies. The hydrogen
thyratron, unlike most thyratrons, has a positive grid-control charac¬
teristic, and hydrogen filling is used to reduce deionization time and make
the performance of the tube independent of ambient temperature. This
independence is maintained with the exception that the average dissipa¬
tion rating of the tube can be lowered by excessively high air temperature.

Sec. 1010]

LINE-TYPE PULSERS

381

The hydrogen-filled thyratron (Fig. 10-41) can satisfactorily pulse at
much higher frequencies than is possible with mercury or other heavy-gas
fillings, because of the high ion mobility inherent in the light-gas filling.
Of course, the average-power rating of the tube must not be exceeded
when going to high pulse rates. In going to high pulse rates, the pulse
width must be decreased faster than 1//, since the average anode drop at
durations of a few tenths of a microsecond is higher than that during a
long pulse. The hydrogen in the discharge seems to require about 10~ 7
sec to become fully ionized, so that a high tube drop is required to deliver
the necessary initial current. It is therefore desirable to reduce the pulse
power output as well as pulse width if tube life is to be maintained at
increased repetition rates. Pulse rates up to 40,000 cps have been
obtained at reduced power output.

Hydrogen thyratrons in production are the 3C45, 4C35, and 5C22,
rated at 25, 250, and 1000 kw respectively; they are shown in Fig. 10-42.
The development of such tubes for still higher power levels is under way.

A nonlinear inductance can also be used as a switch. An inductance
with a special alloy core may be placed between points A'A (Fig. 10-36).
This device has the property of
possessing a high inductance when
the current through it is small, and
a very low inductance when the cur¬
rent is large. Since this type of
switch has generally been used with
a modulated energy source, there is
initially no voltage across A'A and
hence the impedance is high from A'
to A . As the voltage is built up the
current gradually increases until
suddenly, and in a regenerative
way, the impedance of A'A drops,
thereby allowing the line capacity to
discharge through the “switch,” lowering its impedance still more. A d-c
bias winding is sometimes used to control the point at which the impedance
suddenly drops from its high value. Virtues claimed for the nonlinear
inductance switch are long life, ruggedness, and simplicity. The switch
can be operated at pulse repetition frequencies up to 4000 pps and at
power levels in excess of several hundred kilowatts.

The rotary spark gap, because of its great simplicity and high power
handling ability, has been widely used as a switching device. Figure
10-43 shows schematically how a rotating insulating disk pierced by
tungsten pins serves the function of a switch. As the disk revolves and a
rotating pin approaches a fixed pin, the electric field strength becomes

Fixed spark points

Fig. 1G-43.—Rotary spark gap.

382

THE MAGNETRON AND THE PULSER

[Sec. 1010

high enough for breakdown. Current flows from 4' to the disk pin and
out through a second spark at point A. The simplicity of this device is
partially offset by an uncertainty of up to + 50 nsec in firing time, and by
the narrow voltage range over which satisfactory operation occurs. The
display-tube sweeps must be triggered by the appearance of the power
pulse because of the great uncertainty in firing time. If / is the speed of
the disk in rpm, and n is the number of pins, the resulting pulse rate is
»i//60. For a given power output, there is an optimum spacing between
rotating and fixed pins, and a minimum permissible spacing between pins
in the rotating disk. These quantities vary somewhat with disk speed,
so that it is not easy to design a rotary spark-gap pulser for variable pulse
rate.

The Recharging Circuit .—In all forms of network pulsers it is necessary
to recharge the network between pulses. This should not be done at too
rapid a rate. A slow rate of charge is easily obtained by using a large
inductance L 0 , which is also needed to prevent a virtual short circuit
across the energy source every time the network is discharged. Induct¬
ance charging is used in practically all line-type pulsers, because it has
the advantage of high efficiency and permits charging the pulse-forming
network to a voltage nearly double that of the power supply, as shown
below.

Consider first a d-c power supply voltage of negligible resistance, in
series with an inductance, a switch, and a capacity C originally dis¬
charged. The energy supplied by the source in a time T after closing
f T

the switch is Vs L i dt. If Qc is the charge on the condenser, as long as
the energy in the inductance at time T equals that at time 0,

But

Then

•/:

: dt = VsQc = i CVl

Qc = CVc.
VsCVc = i CVl
Vc = 2V S

and the voltage on the condenser C (or pulse-forming network) will be
twice the supply voltage. It must be noted that this result is independ¬
ent of the value of inductance used.

The network voltage obtainable with inductance charging in practice
lies between 1.8 and 1.95 times the d-c supply voltage, because of resist¬
ance losses in the charging reactor. If L 0 and C are the values of charging
inductance and network capacity, “resonance” charging is obtained when
the repetition rate, f T = 1 /(tt \/LoC). If f r > 1 /(*• y/L 0 C), current in

Sec. 10-11]

MISCELLANEOUS COMPONENTS

383

the inductance does not reach zero at the time of firing, and “straight line”
charging results. It is possible to operate a pulser with / r < 1 /(tt v L 0 C)
and still obtain substantially the same voltage step-up, but the network
voltage at the time of firing is less than at some previous time in the charg¬
ing cycle. Because of the undue stresses that are thus placed on the
insulation, as well as the rapid increase in reactor losses, it is common
practice to use, for this case, a “hold-off” or “charging” diode in series
between the inductance and the network, to prevent the flow of reverse
current.

If an a-c supply is substituted for the d-c energy source, the resulting
pulser is inflexible in pulse rate and pulse length, but has the great advan¬
tage of extreme simplicity. It requires neither vacuum tubes nor auxil¬
iary power supplies.

/*[.,

❖

[

v .'f 1

' 1

0 7t 2n 3rr 4/r

0 T 2T

Time t

(a)

Fig. 10-44.—Line-type pulser charging waves. T = charging time; switch fires
at t = T, 2 T, .... (a) Network voltage for d-c resonance charging. Power supply

1 2

voltage = V ,; pulse recurrence frequency = — = ^ ^ - cps; curve x is network voltage if

switch misfires. (6) Network voltage for a-c non-resonance charging under conditions of
maximum step-up ratio. Curve v is impressed a-c voltage; v — E cos (wt — 4>)•

Figure 10-44a shows the voltage waveform across the pulse network
for d-c resonance charging, and Fig. 10-446 for the condition of maximum
one-cycle voltage step-up, which occurs at an impressed a-c frequency
about 0.7 times the resonant frequency l/(x \/L 0 C). A voltage step-up
of about x can be obtained in a single cycle under these conditions, if the
pulser is fired about 21° after the crest of the impressed a-c wave is
reached.

Maximum simplicity is achieved by mounting a rotary spark gap
directly on the shaft of the a-c machine exciting the network. Phasing
is easily accomplished by mechanical adjustment. By proper design,
the transformer used between generator and network can incorporate
sufficient leakage inductance to resonate with the network capacity at
the generator frequency. Pulsers of this type have been very successful;
they are recommended for cases in which specifications are firmly fixed,
suitable repetition rates correspond with available a-c generators, and
the uncertainty in firing time of a rotary spark gap can be tolerated.

384

THE MAGNETRON AND THE PULSER

[Sec. 10-11

10-11. Miscellaneous Components. Pulse Transformers .—The devel¬
opment of pulse switching tubes and of pulse loads has proceeded so
independently that usually there is little correlation between the optimum
impedance levels for best operation of these two devices. Fortunately,
satisfactory pulse transformers are available to match the impedance of
the load to that of the generator. While the elementary theory of the
pulse transformer is quite manageable, great care in design must be
exercised to preserve good wave shape with fast rates of rise, a minimum
of extraneous oscillation, and high efficiency. The ideal transformer is
shown in Fig. 10-45a; Fig. 10 45b shows the equivalent circuit of a prac¬
tical transformer (all values referred to the secondary or high-voltage

Low-voltage High-voltage

end end

( 6 )

Fig. 10-45.—Pulse transformer circuit diagram.

Tip 1 p Tig Z o

(6) Equivalent circuit of pulse transformer.

(a) Ideal transformer; = —

V p rip Ip n,

P = (-)’

Zo \n p J

end), exhibiting the effects of departure from the ideal case. The
symbols shown in Fig. 10-45 are defined as follows:

Li = leakage inductance due to flux from primary current which
fails to link with secondary and represents effect of magnetic
energy stored between windings by load current.

Cd = effect of electrostatic energy stored in the primary-secondary
distributed capacity. If transformer is pulsed from low-voltage
end Cd must be charged through Lj.

L d = “squirted inductance” arising from nonuniform current dis¬
tribution due to the charging of Cd. Current charging C D must
flow through L D .

Cc = effect of electrostatic energy stored between primary and core.

L c = effect of magnetic energy stored in “squirted flux” which comes
from nonuniform current in primary coil arising from the
charging of C c .

L, = effective shunt or self-inductance (input inductance with open
circuit secondary).

R e = resistance due to eddy current in iron and to hysteresis.

A good pulse transformer design attempts to maximize the shunt
inductance L, and minimize the leakage inductance L ( . In addition,
undesirable oscillations arising from the series resonant circuits shown at

Sec. 1011 ]

MISCELLANEOUS COMPONENTS

385

the input and output ends of Fig. 10-455 should be avoided. Leakage
inductance can be kept to a reasonable value by winding the secondary
and primary as close together as voltage breakdown will permit, for the
space between these two windings is responsible for most of the leakage
inductance. The shunt inductance and its magnetizing current con¬
stitute an additional load on the generator which must be minimized by
making L e large.

This last consideration sets a lower limit on the number of primary
turns and also calls for a laminated core with high permeability at high
frequencies. Laminations between 0.001 and 0.005 in. thick are neces¬
sary to maintain a core permeability of several hundred up to the fre¬
quencies of several megacycles per second present in a steep wave front.
Special core materials for pulse transformers were developed during the
war.

A square voltage wave of magnitude V 0 and duration t applied to the
inductance L e wall build up a current of approximately I P = V 0 • l/L e
amperes during the early part of its exponential rise. If this current is
not to exceed a few per cent of the desired load current for pulse lengths
around 1 n sec, L, must have a value between 10 and 20 mh. With this
information, the number of turns in the primary and the required core
area can be obtained from tables showing the effective permeability of the
core at the flux densities and rates of rise anticipated. 1

Since the voltage drop across the leakage inductance is approximately

di ,

Li ■ the maximum permissible value of leakage inductance can be

estimated by assuming that the current in R L must reach 90 per cent of
its final value, Vo/Rl, in a time of about to/10. The current which flows
must satisfy the equation

To a sufficient approximation, La = R t t r •

where I/I 0 is the fraction

of final current built up in the rise time t T . If 1, = 0.1 X 10 -6 sec,
Rl = 1000 ohms, and I/I 0 = 0.9, L t must be less than 100 ^h.

Satisfactory high-power (100-kw to 5000-kw) pulse transformers
have been designed which pass good wave shapes down to to = 10 -7 sec
and up to to = 10~ b sec, but it is quite difficult to design a pulse trans¬
former to pass a wide range of pulse lengths. Although a long pulse calls
for a large value of L„ large L, magnifies the difficulties of securing the
small value of L t required to pass a very short pulse. Transformers have
been designed which satisfactorily pass pulse widths varying by a factor
of 10; pulses of shorter or longer duration than the optimum suffer either

1 See Pulse Generators, Vol. 5, Radiation Laboratory Series, Chaps. 12 to 15.

386

THE MAGNETRON AND THE PULSER

[Sec. 10-11

in rate of rise or in flatness of top. Wider-range transformers will be
practical only when higher permeability cores and stronger insulation
with lower dielectric constants are available.

Insulation between windings and adequate cooling must also be taken
into account in design. High-power transformers lend themselves most
readily to oil insulation because of the insulating and convection-cooling
properties of the oil. In the lower-power range (200 kw and down) it is
usually convenient to use solid dielectric materials, with a consequent
saving in weight and size. Figure 10-46 shows the variation in size of a
pulse transformer vdth power output. As in the case of pulse networks,

Fig. 10-46.—Pulse transformers.

the size and weight of a pulse transformer depends not only upon the
pulse power to be handled, but also upon the*pulse length and the repeti¬
tion rate. These, together with the transformer efficiency, determine the
amount of average power which must be dissipated by the transformer.

A pulse transformer contributes a certain amount of undesirable
inductance and capacity to the pulser circuit. Special damping devices
may be necessary to remove unwanted oscillations. Damping resistors
and appropriately phased diodes are ordinarily used for this purpose.

Pulse Cables .—In handling high-power pulses with steep wave fronts,
extreme care must be taken to shield the equipment sufficiently to prevent
the radiation of signals which interfere with the operation of communica¬
tions receivers and other electronic equipment. This shielding is espe¬
cially necessary when the pulse must be transmitted several yards between
pulser and load. Existing pulse transmission cables and their connectors
provide satisfactory shielding and resistance to voltage breakdown, but
are still rather bulky, hard to assemble, and heavy. Considerable
improvement in their detailed design can be hoped for.

Sec. 10-llJ MISCELLANEOUS COMPONENTS 387

Energy Sources .—The energy source accounts for most of the weight
and much of the complexity of any pulser except those of the a-c resonance
charge type. All conventional types of rectifier circuit can be used in
pulser power supplies. The only design considerations arising from the
nature of the pulser load are those governing ripple and regulation. In
general, the a-c supply frequency will be less than the pulse rate, and
smoothing condensers capable of holding the voltage essentially constant

Fig. 10-47 —Low-power airborne pulser.

between pulses must be used. For example, a 60-cycle full-wave rectifier
is brought to full voltage only 120 times per second, so that a pulse rate
of 1200 cps would draw 10 pulses of power between successive recharge
cycles. In figuring ripple it is usually satisfactory to assume a constant
rectifier drain equal to the average current required by the pulser. The
ripple must be kept below that which would cause a change in magnetron
current sufficient to produce either a mode shift or undue frequency
modulation. Apart from this consideration, amplitude modulation is

388 THE MAGNETRON AND THE PULSER [Sec. 1011

harmful only in those radars which detect moving targets (see Chap. 16)
by comparing successive pulse phases.

We have already remarked that pulser internal impedance may some¬
times play a deciding role in mode stability. It is also true that the power
supply steady-state V-I characteristic may influence magnetron behavior.

Fig. 10-48.—Medium-power airborne pulser.

A mode change in which an increase in voltage calls for a decrease in cur¬
rent can cause the instability typical of any negative-resistance load. 1
It is of considerable importance that the designer consider the problem of
stability from the standpoint of the system as a whole.

The necessity of providing for a varying pulser load influences
rectifier and power-supply design. It is frequently desirable to change
the repetition rate of the pulser. This change is easy in principle, but in
1 RL Report No. 809, Sept. 28, 1945.

Sec. 1011]

MISCELLANEOUS COMPONENTS

389

practice many annoying points must be considered, including tempera¬
ture shift, change in back-bombardment heating of the magnetron
cathode, change in pulser starting delay, and change in rectifier voltage.
The usual practice is to change the pulse lengths inversely with the pulse
rate, thus keeping average power constant. But, because of the com¬
plications inherent in changing pulse length by switching pulse networks,
the pulser designer is always inclined to stick to one pulse width. If
pulse rate must be changed without a compensating change in pulse

Fio. 10-49.—High-power airborne pulser.

width, it is usually necessary to control the rectifier output by switching
power transformer taps or by varying a series primary impedance.

The present design of high-voltage, low-average-current rectifying
diodes is quite satisfactory. There are now available diodes of reasonable
dimensions, high inverse rating, and good life, covering most practically
useful ratings. Thoriated tungsten cathodes are universally employed;
these have satisfactory mechanical strength and are economical of
filament power. Efficiency could be further increased by the develop¬
ment of a filamentless rectifier. This would permit operation without
filament transformers which, in some circuits, must be insulated for high
voltage. Perhaps a cold cathode discharge tube, or a barrier-layer
rectifier, will one day replace the filamentary rectifier.

' Line-type pulsers for radar applications have been built and operated
successfully to cover a range of pulse power output of 1 kw to 20 Mw.
The following photographs show typical pulsers designed for airborne
service.

Figure 10-47 shows a hydrogen-thyratron pulser designed to supply

390

THE MAGNETRON AND THE PULSER

[Sec. 1011

25 kw to the magnetron, at pulse durations of 0.8 nsec and 2.2 Msec. The
components weigh approximately 6 lb.

Figure 10-48 shows a hydrogen-thyratron pulser designed to supply
225 kw to the magnetron, at pulse durations of 0.25, 0.5, 2.6, and 5.2
nsec. The weight of components is about 40 lb.

Figure 10-49 shows a fixed-gap pulser designed to supply 2 Mw to the
magnetron at a pulse duration of 2 Msec. The complete pulser, including
pressurized housing and cooling system, weighs around 300 lb.

MR. is ■ ' ■

173 ' ' ON RO --3

AUP-UBON 6, N. J-

CHAPTER 11

R-F COMPONENTS

By A. E. Whitford

11»1. The R-f Transmission Problem.— In the block diagram of a
basic radar system shown in Fig. T4, the parts shown as heavy double
lines transmit the radio-frequency (r-f) energy from the magnetron to the
antenna, and carry the faint echo signals into the T-branch where the
receiving apparatus is located. For the types of radar treated in this
book this function is performed by coaxial lines and waveguides. A
considerable body of theory and a new set of techniques have grown up
around this class of transmission circuits. The essential new feature is,
of course, that the wavelengt h is of the same order as the physical size of
the circuit elements; the length of the line may be many wavelengths.
Although space permits only a limited treatment here, 1 sufficient intro¬
duction will be given to show the general approach, and to make under¬
standable some of the reasons for current practices in microwave radar.

Standing Waves .—When a voltage is suddenly applied to the input
terminals of a long and uniform transmission line, the current which flows
in the initial interval, before reflections from the far end arrive to confuse
the situation, is determined by the property of the line known as its
“characteristic impedance.” The characteristic impedance, Z 0 , is a
function of the geometry of the conductors and insulators of the line, and
for good conductors and low-loss dielectrics is almost purely resistive.
For a concentric line, neglecting losses,

Z 0 = —p logm — ohms

V« T l

where k is the dielectric constant of the material in the annular space
between the conductors, r 2 is the inner radius of the outer conductor, and
ri is the outside radius of the inner conductor.

A uniform line terminated at any point in its characteristic impedance
behaves as if the line were infinitely long; there is no reflection. Power
introduced at the input terminals disappears into the termination with
small losses in the line. However, any discontinuous change along the

1 More extended treatment can be found in other books of this series, especially
(1) Microwave Transmission Circuits, Vol. 9; (2) Microwave Duplexers, Vol. 14;
(3) Waveguide Handbook, Vol. 10; (4) Principles of Microwave Circuits, Vol. 8.

391

392

R-F COMPONENTS

[Sec. Ill

line, such as might be introduced by a change in dimension of one of the
conductors, or any change in geometry introduced by a sharp bend, or
by a dent or an obstacle in the line, will produce a reflection. The
reflected energy travels back toward the source. This results in standing
waves in the line. These can be observed by sliding a small probe along
a slot in the line after the manner shown for a concentric line in Fig. 11 1.

Only a negligible fraction of the
power is abstracted by the probe,
but, fed into a suitable indicator,
this is sufficient to register the volt¬
age variations along the line. In
general there will be voltage maxima
spaced at half-wavelength intervals
with minima halfway between them.
Only if the line is perfectly matched will the voltage reading be constant as
the probe moves along. The ratio of the maximum to the minimum volt¬
age is called the “voltage standing-wave ratio” (VSWR) and is the usual
criterion of how well a line is matched. Complete reflection at the end
of the line, such as would be expected from an open circuit or a short
circuit, results in zero voltage at half-wave intervals and a VSWR of
infinity. The mismatch may also be expressed as a power ratio (PSWR),
or in decibels. The relations between these three measures are

PSWR = (VSWR) 2
SWR, db = 10 log 10 (PSWR).

Quarter-wave and Half-wave Lines .—It can be shown that when a loss¬
less transmission line of characteristic impedance Z 0 a quarter wavelength
long is terminated in an impedance Z t , the input impedance is

Zi — Zl/Zu (1)

This property is widely used. For example, two transmission lines of
differing impedance can be matched to each other by joining them through
a quarter-wave line whose characteristic impedance is the geometric
mean of that of the two lines. This is called a matching transformer.
Or, if a quarter-wave line is terminated by a short circuit, the input
impedance is infinite, i.e., equivalent to an open circuit. Conversely,
an open-circuited quarter-wave line appears at the input terminal to be
a short circuit. For a lossless line half a wavelength long

Zi = Z t , (2)

irrespective of the characteristic impedance of the line. This principle
has many uses also, particularly in duplexers (Sec. 11-5) and mixers
(Sec. 11-8).

Fig. 11*1.—Slotted coaxial line and
probe for observing standing waves (cuta¬
way view).

Sec. 11-2] COAXIAL LINES 393

Why a Matched Line ?—The fraction of the incident power reflected
to the source from a section of transmission line of given VSWR is

Power reflection coefficient = [ (VSWR) + lp ( 3 )

For the usual upper design limit of VSWR = 1.5, it is seen that the power
reflection loss is only 4 per cent, or 0.3 db, surely not serious. In high-
power systems or unpressurized airborne systems, where line breakdown
is a possibility, the strain is of course higher for a high VSWR. A ratio
of 1.5 means that for a given breakdown gradient, 33 per cent less power
can be delivered to the load than could be delivered in a matched load.
This can be a limitation.

The strongest requirement for a well-matched line arises from the
properties of the magnetron. Like all self-excited oscillators, the mag¬
netron exhibits an output frequency and a stability dependent upon the
load into which it works. A mismatched line represents a resistance
lower than Z 0 at voltage minimum, and higher than Z 0 at voltage maxi¬
mum. At other phases it has a reactive component which may be either
positive or negative. As explained in Chap. 10, magnetrons are in gen¬
eral designed to be stable against a VSWR of 1.5 in any phase. This is
the origin of the commonly specified upper limit for mismatch.

There is a further limitation if the mismatch occurs at the end of a
long line—for example 50 to 100 wavelengths from the magnetron. Then
as the frequency changes the number of wavelengths in the line changes,
and so also does the phase of the standing wave. The line impedance
seen at the magnetron is therefore a rapidly varying function of frequency.
If at a certain frequency the phase happens to be such that the variation
of reactance of the line with frequency is more rapid than that of the
magnetron itself, and of opposite sign, a condition results where the mag¬
netron has no stable frequency. In another, favorable, phase the mag¬
netron is stabilized. This is known as the “long line effect.” 1 The
result is that for long lines either (1) VSWR’s lower than 1.5 are necessary
to guarantee stable magnetron operation, or (2) a method of changing
the effective line length and hence the phase of the standing wave must
be included in the antenna line. The latter may be done by a “line
stretcher” not unlike a trombone, or in waveguide by a squeeze section
or a dielectric phase shifter. 2 These add an undesirable adjustment.

11-2. Coaxial Lines. —Coaxial lines consisting of concentric inner
and outer conductors are not new. At lower frequencies they have
usually consisted of cables with a solid dielectric and a braided outer

1 Microwave Magnetrons, Yol. 6, Radiation Laboratory Series.
a Microwave Transmission Circuits , Yol. 9, Radiation Laboratory Series.

394

R-F. COMPONENTS

[Sec. 11-2

conductor. These are used at microwave frequencies also, especially for
short, low-power interconnecting cables in the 10-cm region. However,
the attenuation even in the best dielectric, as seen in Table 11 1, begins
to be serious at 10 cm and gets worse at shorter wavelengths. Substitu¬
tion of air for the solid dielectric eliminates dielectric losses, and only the
much smaller conductor losses remain. But the center conductor must
somehow be supported mechanically. Thin dielectric beads have been
used as supports, but the disintegrating effect of dielectric breakdown
over the surface of the bead is hard to avoid. Reflections from the beads
can be largely canceled by proper spacing. 1 However, bead-supported

Table 11 1.—Standard Microwave Transmission Line

Maximum

Attenua-

Wave-

Dimensions OD, in.

Wall, i:i.

length, cm

power, *
Mw

tion,f

db/m

length
range, cm

A. Waveguide

H X 3

0.080

10.0

10.5

0.039

7 . 6 - 11.8

t X If

0.061

3.2

1.77

0.15

3.0-4.7

1 X 1

0.050

3.2

0.99

0.24

24-3.7

i X h

0.010

1.25

0.22

0.5f

1.1-1.7

B. Rigid coaxial lines, stub-

supported

Outer If

0.049

10.0

4.2

0.08

9.3-11 .7

Inner |

0.035

Outer }

0.032

10.0

1.3

0.15

9.1-11.7

Inner f

0.032

Outer f

0.032

3.2

0.36

0.49

3.1-3.5

Inner -fa

0.032

C. Flexible coaxial cable, RG-

9/U, polyethylene dielec¬
tric

Dielectric OD 0.280 in.
Inner conductor 7 strands

no.o

0.31§

0.561

3.0- 00

#21 AWG,

Outer conductor double

l 3.2

0.31§

1 . 12 )

braid

* Computed for maximum gradient of 30 kv/cm. No allowance in coaxial lines for increased field
around stub supports. Practical operating point § to J of values given.

t For brass wall9. For copper or silver walls, attenuation is about half that listed, and for silver
plating has an intermediate value, depending on finish.

t Experimental value for coin-silver tubing, generally used at this wavelength. Surface finish
affects value.

§ Specification limit for cable alone. Connectors limit safe power to a few kilowatts.

1 Microwave Trammission Circuits, Vol. 9.

Sec. 11-2]

COAXIAL LINES

395

lines have been almost completely supplanted by stub-supported lines
in the 10-cm region.

The principle of the stub support is shown in Fig. 11-2. As was men¬
tioned in Sec. 11-1, the input impedance of a quarter-wave line shorted
at the far end is the same as an open circuit. When placed in parallel
with the main line such a connection has no effect at all on the impedance

Fia. 11-2.—Simple quarter-wave stub Fig. 11*3.—Broadband stub support,

support.

and causes no reflection. The mechanical and electrical superiority of a
solid piece of metal as a support and insulator is obvious, and at 10 cm
the length of the stub (about 1 in.) is such as to make the projection short,
and unobtrusive.

Obviously a quarter-wave stub can have the desired property at only
one frequency. Deviations of only 1 to 2 per cent in frequency cause the
stub to have a reactance that pre¬
sents an appreciable mismatch.

Figure 11-3 shows a broadband stub
support where the frequency sensi¬
tivity is compensated over a band of
+ 15 per cent. At the center of the
band the stub has an effective length
of exactly a quarter wave, and the

two quarter-wave sections in the Fig . 11.4.—stub-supported elbow,

main line transform to an impedance

low'er than normal and then back to normal. The conditions for no reflec¬
tion are satisfied. At a frequency lower, for example, than the center fre¬
quency, the stub is less than a quarter wave, but the inductive reactance
thereby presented at the T-junction is made just enough to compensate
for the fact that the quarter-wave transformers in the main line are also
less than a quarter w-ave long, and would present a mismatch in the
absence of the stub. Similar, but converse, conditions obtain for fre¬
quencies higher than band center. Figure 11-4 shows how a broadband
stub can be used to make an elbow. There is an added complication
because the sharp elbow introduces a reactance which must be compen¬
sated for in the construction of the stub.

Such supports are standard in coaxial lines used in the 10-cm region
and regularly have a VSWR less than 1.03 over a band of +15 per cent
from the center frequency.

396

R-F COMPONENTS

[Sec. 11-2

The standard connector for joining coaxial lines is shown in Fig. 11-5.
Since longitudinal currents cross the junction plane on both inner and
outer conductor, good contact must be assured. For the outer conductor
this is done by pulling together two mating cones of differing taper by
means of the strong outer clamping rings. The fittings that solder to

Fia. 11-5.—Coupling for coaxial line.

the outer tube also contain a gasket groove for keeping the line airtight.
The inner conductor is itself a tube. The two pieces are joined by a
beryllium copper “bullet” which is soldered into one piece and makes
tight contact with the inner surface of the other by means of expanding
prongs on the rounded tip.

In order to transfer r-f power to a rotating scanner, a rotary joint for
a coaxial line is necessary. Early designs involving wiping contacts on

both the inner and outer conductors
gave difficulties arising from poor con¬
tact, sparking, and wear. The superi¬
ority of the noncontact type employing
choke joints has led to its universal
^ adoption. The principle is shown in its

simplest form in Fig. ll-6a. The gap
between the stationary and rotating
BMjgg ffiTN parts of both conductors is situated at

the end of an open-ended quarter-wave
S - - coaxial line. As was mentioned in

1 " Sec. 11*1, the impedance at the input

end of an open quarter-wave section (in
. . , this case across the gap in the line) is

Fig. 11*6.—Choke-type rotary joints. . t _

zero, rower nows across without loss
or sparking. Closer analysis shows that the open end of the quarter-
wave section on the outer conductor is not an infinite impedance, because
there is some radiation, producing a finite radiation resistance. This
effect can be reduced, and the match improved, by adding a short-cir¬
cuited quarter-wave line in series with the outer gap, as in Fig. 11-66.
The outermost gap can now be very small, or even a rubbing contact,

Sec. 112]

COAXIAL LINES

397

since no current flows across it. A similar improvement is made on the
center conductor. Advantage is taken of the negligible current across
the transition between the first and second quarter-wave sections to make
a contact bearing between the innermost conductors. This is a great aid
in keeping the closely spaced tubes all concentric. Quarter-wave line
sections used in the manner just described to prevent loss of microwave
energy into side channels are termed “chokes.”

The nominal characteristic impedance of the standard rigid coaxial
lines in regular use is 50 ohms, corresponding to a ratio of 2.30 for the
radii of the inner and outer conductors. This is a compromise between
a ratio of 3.60 (77 ohms), which, for a given outer diameter, gives the
lowest attenuation due to conductor losses, and a ratio of 1.65 (30 ohms)
which maximizes the power that can be carried 'with a given breakdown
voltage gradient. Since the attenuation in a 50-ohm line is only 10 per
cent greater than it is in a 77-ohm line, it is not a costly compromise.
Increasing the size of both conductors to increase the air gap and thereby
increase the power-carrying capacity cannot be carried on indefinitely,
since a higher mode of propagation,
with diametral rather than axial
symmetry, can be excited when the
mean circumference of the annular
dielectric space exceeds one wave¬
length. The possibility of two
modes of propagation existing
simultaneously in a single line leads
to serious complications. The high¬
est powers are best transmitted by
means of waveguide.

Rigid coaxial lines are not ordinarily used for wavelengths below 8 cm
because the limitation on over-all size just mentioned permits too low a
maximum power-carrying capacity. However, a standard i-in. OD
stub-supported line with appropriate couplings has been worked out for
the 3-cm band. The largest stub-supported standard coaxial line is in
lf-in. OD tubing, with stubs designed for the 9- to 11-cm band; the
higher-mode limit prohibits anything larger on this band. For moderate
powers, i-in. OD line with stubs designed for the 9- to 11-cm band is
standard. The theoretical breakdown power for the i-in. line, assuming
sea-level pressure and a maximum field of 30 kv/cm, is 1.3 Mw. How¬
ever, nonuniform fields around stubs and the increased gradient in the
chokes on the inner conductor of rotary joints make the safe engineering
design limit about 0.3 Mw.

The type of flexible coaxial cable most commonly used in the micro¬
wave region (Army-Navy designation RG-9/TJ) has a polyethylene

398

R-F COMPONENTS

[Sec. 11 3

dielectric of nominal outer diameter 0.280 in. A section of the cable with
the standard type N connector is shown in Fig. 11-7. The connectors
match the 50-ohm impedance of the cable at 10-cm and longer wave¬
lengths. The mismatch at 3 cm is not great. Breakdown in the con¬
nectors limits the peak power to a few kilowatts; the most common use
of such cable is in test equipment. Attenuation data are given in
Table 11 1.

11-3. Waveguide. —Although a metallic pipe of almost any shape
will transmit or guide electromagnetic waves if their wavelength in air is
short enough, rectangular tubing whose internal dimensions have a ratio
between 2.0 and 2.5 has been almost universally adopted where the prob¬
lem is simply the transfer of microwave energy. (Use of round guide in
the special case where axial symmetry is required is discussed in a later
paragraph.) A detailed understanding of the propagation of waves in a
region bounded by conducting walls can only be obtained from the solu¬
tion of Maxwell’s equations. Practically, however, the results of the
mathematical analysis 1 have come to be used in a procedure which retains
most of the concepts of transmission-line theory, with equivalent lumped
reactances connected at suitable points to account for the effects of
discontinuities.

The resemblance between a rectangular waveguide and a two-wire
transmission line is shown in Fig. ll-8a to ll-8d. In Fig. 11-8a is shown
a single quarter-wave stub support, analogous to the coaxial stub support
described in Sec. 11-2. At the proper frequency the input impedance of
the short-circuited stub is extremely high and there is no effect on the
propagation of the wave on the line. In Fig. 11-86 a great many stubs,
extending both ways from the two-wire line, have been added, still with¬
out affecting the propagation of the frequency in question. In Fig. 11 -8c
the stubs have coalesced into a rectangular tube which looks like a wave¬
guide. For a single stub, a slight correction to the length is necessary to
allow for the inductance of the crosspiece, but when the stubs become a
solid tube, no lines of force can link the narrow side, and the quarter-
wave distance becomes exact. This also implies that the length of the
narrow side of the tube is not critical.

The two-wire transmission-line model explains how a waveguide can
transmit all frequencies higher (wavelengths shorter) than that for which
the quarter-wave stubs were designed. In such a case, as shown in Fig.
ll-8d, the two wires become broad busbars with only as much of the wide
side of the guide given over to stubs as is required by the now shorter
wavelength. However, wavelengths greater than twice the broad
dimension cannot be propagated because then the stubs become less

Waveguide Handbook, Vol. 10; Microwave Transmission Circuits, Vol. 9.

Sec. 11 3]

WAVEGUIDE

399

than a quarter wave and shunt the line with a rather low inductive
impedance which would stop transmission.

Fig. 11 8.—Waveguide derived from stub-supported two-wire transmission line.

Fig. 11-9.—Fundamental mode of wave propagation in a rectangular guide; (a) and ( b )
show the electric field in a transverse and longitudinal cross section; (c) shows the lines of
current flow in the top and side of the waveguide as long dashes; the dotted lines represent
tangential magnetic field at the wall.

Figure 11-9 shows an instantaneous picture of the electric and mag¬
netic fields in a rectangular waveguide whose wide dimension is slightly
over half the free-space wavelength. The lines of current flow in the

400

R-F COMPONENTS

[Sec. 11-3

walls are also shown. At all microwave frequencies, the skin effect
confines the current to a microscopically thin layer on the inner surface.
As the dimensions of the waveguide are increased, the frequency being
fixed, propagation becomes possible by modes —that is, by particular
types of “vibration” in the electromagnetic field, other than the funda¬
mental mode illustrated in Fig. 11-9. Each of these higher modes has
its own characteristic electromagnetic field configuration. Ordinarily
it is advisable to avoid propagation in more than one mode, and this is
most easily done by choosing the dimensions of the guide so that the
lowest mode, and the lowest mode only, can propagate. However, for
certain applications some of the higher modes are useful. A notable
example, to which we shall return later, is the second mode in waveguide
of circular cross section. This has axial symmetry and is thus useful in
waveguide rotary joints.

For each type of waveguide there exists a critical, or cutoff, frequency
for propagation in the lowest mode. Waves of higher than critical fre¬
quency are transmitted; those of lower frequency are rapidly attenuated. 1
Corresponding to the cutoff frequency j c is a cutoff wavelength X„ related
to /„ by X„ = c/fc where c is the velocity of light. That is, X„ refers to the
wavelength in space. For rectangular guide, as shown from the stub-
supported two-wire line, the cutoff wavelength is twice the broad dimen¬
sion. In other words, a guide that is to transmit a wave must have a
broad dimension greater than half a free-space wavelength. If the width
is more than a whole free-space wavelength, a higher mode of propagation
with a node in the electric field down the center becomes possible, which
adds most undesirable complications. Therefore, the broad dimension
must lie between a half and a whole free-space wavelength. The wave¬
length inside the guide is longer than that in free space and is given by the
relation:

Guide wavelength = X„ = —(4)

where X is the free-space wavelength and X c is the cutoff wavelength (here
equal to twice the broad dimension). When X c is only slightly greater
than X, the guide-wavelength becomes very long and varies rapidly with
changes in X. This greatly increases the frequency sensitivity of quarter-
wave sections of guide used in duplexers and mixers (Secs. 11-5 and 11-8)
and handicaps broadband design. The other extreme of a close approach
to the boundary of the higher mode, corresponding to a wide dimension
of nearly a whole free-space wavelength, runs into difficulty because of

1 In a waveguide beyond cutoff the voltage or current falls off exponentially with
distance, with constants exactly calculable from the dimensions and frequency. One
form of standard attenuator utilizes this fact.

Sec. 11-3]

WAVEGUIDE

401

too gradual an attenuation of the higher modes inevitably excited at
discontinuities such as T-junctions and diaphragms. For these reasons,
waveguides are ordinarily used only for frequencies where the broad
dimension lies between 0.60 and 0.95 of the free-space wavelength.

Since the maximum electric field comes across the narrow dimension
of the guide, it is undesirable to choose this dimension too small. In
fact, the power that can be transmitted for a given breakdown field is
directly proportional to the guide di¬
mension in the direction of the field.

The height is limited by the require¬
ment that the narrow dimension be
less than half a free-space wavelength
in order to avoid the possibility of
propagating the simplest mode hav¬
ing polarization at right angles to FlG ' n-io.-Wave^deAoke coupling,
that shown in Fig. 1T9.

There is no unique or generally accepted definition of the impedance
of a waveguide. This might be expected from the lack of definite
localized terminals at which the voltage and current could, in principle
at least, be measured. However, the usual procedures of impedance¬
matching are carried over from transmission-line theory, and calculations
are made on the basis of normalized impedances. The impedance of a
standard waveguide is defined as unity, and resistive or reactive elements
inserted in the guide are computed relative to the standard, rather than
in ohms.

A typical choke joint between pieces of waveguide is shown in Fig.
11-10. The principle is identical with that discussed in Sec. 11-2 for the
outer conductor of a coaxial rotary joint. The diameter of the radial
section spreading out at right angles to the rectangular tube is chosen so
that the average or effective distance from the inner surfaces of the
waveguide is a quarter wavelength. A circular groove, likewise a quarter
wavelength deep, forms the short-circuited terminating section. A rub¬
ber gasket in the outer groove serves to keep the waveguide airtight. By
careful choice of dimensions, such a joint can be made to be a good match
over a frequency band 12 to 15 per cent wide. Since no current flows
across the gap between the choke and its mating flange, physical contact
is not necessary. The power flows across a small gap with negligible loss.
However, in such a case the leakage of radiation, although small compared
to the transmitted power, may still overwhelm sensitive energy detectors
nearby. In cases where electrical leakage must be minimized and the
outer gasket groove is not needed for pressurization, an electrical gasket
is substituted. Such a gasket is made by pressing a ring of woven metal
gauze into the proper form.

402

R-F COMPONENTS

'S"C. 11-3

Contact-type unions have also been used successfully. The flanges
are relieved so that the bolts bring maximum local pressure to bear near
the junction of the waveguide walls. Abrasion of the mating surfaces
is much more serious in such a union than in the choke-type joint.

Bends in waveguide such as those in Fig. ll llo cause inappreciable
mismatch if the inside radius is greater than twice the free-space wave¬
length. Short-radius bends are well matched if the length along the
center of the guide is half a guide wavelength. Such elbows as those
shown in Fig. 11-llc, are produced by electroforming—that is, plating
copper or other metal on a soft metal mold which is later melted out.
Two-cut miter elbows, such as those shown in Fig. ll-llb, are well
matched if the distance between cuts, measured along the center of the
guide, is a quarter of the guide wavelength. Flexible waveguide can be
made by winding it up out of metal strip in the same way that certain

Sec. 11 31

WAVEGUIDE

403

types of metal hose or conduit are produced. A molded rubber sheath
pressurizes and protects the piece, as well as holding the adjacent turns
in tight contact. For short lengths, convolutions small compared with
the wave-length can be formed hydraulically, and thereby give flexibility
to a continuous metal tube. Figure 11-lid shows an example.

Transitions between waveguide and coaxial lines usually take the
form of a quarter-wave stub antenna on the coaxial line projecting into
the waveguide a quarter guide-wavelength from an endplate, as shown in

waveguide. (6) Doorknob transition.

Fig. 11-12a. The endplate reflects the energy going in that direction
back in phase with that going down the guide. Expressed in terms of
impedances, the short-circuited quarter-wave section of guide presents
an open circuit at the probe. Then the load seen at the probe is only a
single unit of guide impedance, rather than two units in series. Such a
probe lowers the breakdown potential of the guide. The “doorknob”
transition of Fig. 1112f> is designed to minimize breakdown. It can be
thought of as a quarter-wave probe with a special form of stub support
for the tip of the probe in which capacitive and inductive effect have been
balanced against each other so that as a support it presents no loading
of the waveguide. Rounded contours reduce the electrical gradient as
much as possible.

Rotary joints between pieces of waveguide may consist of a coaxial
rotary joint of the type described in Sec. 1T2 with transitions to wave¬
guide at each end. This is common in the 10-cm region. The large
lf-in. OD line and the doorknob transitions just mentioned are used

404

R-F COMPONENTS

[Sec. 113

where powers of the order of a megawatt are handled. In the 3-cm
region transition is made to round guide, where the next-lowest mode has
axial symmetry. Currents flow across the junction between the rotating
and nonrotating parts of the round tube by means of the same folded
choke arrangement used for the outer conductor of the coaxial rotary
joint described in Sec. 11-2. Figure 11-13 shows a typical joint. The
lowest mode in round guide has diametral rather than axial symmetry,

and if present to an appreciable extent will cause serious variation in
voltage standing-wave ratio as a function of angle of rotation. The
transitions from rectangular to round guide are designed to avoid exciting
the undesired mode as far as possible. The guide wavelengths of the
desired and undesired modes are sufficiently different so that a suitable
choice of length of round guide will minimize coupling of the undesired
mode from one rectangular guide to the other. Various absorbers for the
undesired mode are sometimes used.

The power-handling ability of a waveguide, calculated from the electric
fields involved, is approximately twice that of the largest coaxial line that

Sec. 11 -4]

RESONANT CAVITIES

405

could be used for the wavelength carried by the waveguide. Since, how¬
ever, the distortion of the normal field by the stub supports of the coaxial
line makes it impossible to realize the calculated limit, the factor of two
does not represent the full superiority of waveguide. In either waveguide
or coaxial line, small nicks, burrs, or solder fillets can easily cause break¬
down at a fifth of the calculated maximum power. Table 11T sum¬
marizes the properties of the waveguides widely used in microwave radar,
and for comparison those of some standard coaxial lines and cable.
Attenuation in waveguide is seen to be about half that in the largest
coaxial line suitable for a given wavelength. For smaller coaxial lines
of a given impedance the attenuation is inversely proportional to
diameter. The conclusion to be drawn is that waveguides are superior
electrically to coaxial line in nearly every respect. They are easier to
fabricate because the inner conductor and its precisely machined stub
supports are simply omitted. For these reasons, waveguide is almost
universally used for wavelengths below 8(cm. In the 10-cm region where
the size and weight of the li- by 3-in. waveguide are awkward and the
power-carrying capacity is not needed, coaxial line is frequently used.
For “long wave” radars (wavelengths of 50 cm and greater) waveguide
is never used because of its relatively enormous size.

11-4. Resonant Cavities. —If both ends of a waveguide are closed
by a short-circuiting plate, and energy is introduced by a probe so small
that it does not appreciably change the properties of the enclosure, the
amplitude of the standing-wave pattern in the waveguide will show a
sharp maximum when the frequency is such that the length of the
enclosure is an integral number of half guide-wavelengths. The reflec¬
tions will then be in the proper phase to reinforce each other and cause a
resonant buildup. (This is the property used in wavemeters.) For
standard rectangular guide, reference to Eq. (4) shows that if the broad
dimension is taken to be 0.707X then half a guide-wavelength is also
0.707X. The shortest resonant piece of such a waveguide is therefore
square. The height does not affect the resonant wavelength, though if
it is greater than X/2, modes polarized at right angles to the desired mode
become possible. Rounding off the corners of the square box shortens
the resonant wavelength slightly; exact calculation shows that for a
cylindical box the resonance occurs when X = 1.30 times the diameter, as
opposed to 1.41 times the side of the square.

These round and square boxes are examples of resonant cavities, which
play the same role in microwave transmission circuits as do resonant cir¬
cuits involving lumped inductance and capacity in traditional circuit
theory. Any hollow metal enclosure is capable of supporting oscillations
in a large number of modes. In practice the geometry is usually chosen
so only a single mode, often the lowest, is excited. For simple geometri-

406

R-F COMPONENTS

[Sec. 11-4

cal forms the properties are completely calculable from Maxwell’s
equations.

In cavities of the type used in magnetrons, the inductance and
capacity are fairly well separated and approximate numerical values can
be calculated though they cannot be measured independently. For
something like a simple cylindical cavity, however, inductance and
capacity are blended and cannot even be calculated unambiguously.
The significant quantity is the resonant frequency or wavelength.

The second property of cavities that is important in microwave work
is their Q. As in lumped-constant circuits, the value of Q is a measure
of the sharpness of the resonance, and is determined by the dissipative
elements loading the resonant circuit. If f 0 is the resonant frequency and
/i and / 2 are the “half-power points,”—that is, the two frequencies, one
above/o and one below/ 0 , at which the voltage (or current) in the cavity
is 0.707 as great as it is at resonance—then

Q =

/i — /a

( 5 )

An equivalent, but somewhat more general, formula for Q involves
the amount of electromagnetic energy stored in the oscillating field within
the cavity, and the rate at which energy is dissipated in the walls or in
any other way. If we denote the total stored energy by IF, and the
energy dissipated during one r-f cycle by w, Q is given by

Q =

2irW

(6)

If w includes only the dissipation within the cavity itself, due to the
resistance of the walls and to dielectric losses in insulators within the
cavity, etc., the Q defined above is called the unloaded Q, usually written
Qo. If w includes, in addition, energy dissipated in external circuits
coupled to the cavity, we obtain instead the loaded Q, or Q L , which of
course can never exceed Qo-

In a simple cylindrical cavity made of copper and resonant at 3000
Mc/sec in its lowest mode, the unloaded Q is about 15,000. Generally,
the Q of a cavity loaded only by the resistance of its walls depends on the
ratio of the volume of the cavity to the product of the internal surface
area and the skin depth. For cavities of similar shape, the resonant fre¬
quency fo is inversely proportional to a linear dimension of the cavity;
the skin depth varies as l/V/o- It follows that Q 0 , for cavities of similar
shape, varies as 1/vTo- On the other hand, the Q values that can be
attained at microwave frequencies, typified by the example just given,
are much higher than can be realized with coil and condenser combina-

Sec. 11 - 5 ]

DUPLEXING AND TR SWITCHES

407

tions at low frequencies. The essential reason for this is that such low-
frequency circuits do not provide a correspondingly large volume for the
storage of energy.

To make a cavity useful it is necessary to provide some means of
introducing and removing energy, or in other words to couple it to the
external circuit. This may be done by an electron stream, by a coupling
loop to a coaxial line, or by an iris (hole) leading into a waveguide.
Examples of these are cited in the discussion of klystrons (Sec. 11-7) and
of TR switches (Sec. 1T5).

11-5. Duplexing and TR Switches. —As was explained in Sec. T3,
the use of a common antenna for
transmitting and receiving requires
fast-acting swatches 1 to disconnect
the receiving apparatus from the
antenna during the transmitted
pulse, and to disconnect the mag¬
netron during the period when
echoes are being received. These
two switches are called the TR
(transmit-receive) switch and the
anti-TR or ATR switch, respec¬
tively. The duplexer is that por¬
tion of the microwave circuit, near
the T-junction of the receiving branch and the magnetron-antenna line,
where the TR and ATR swatches are located.

The great disparity in transmitted and received powers immediately
suggests that a spark gap or gas-discharge tube can be connected in the
circuit in such a way as to perform the necessary switching operations.
These gas-discharge tubes are referred to as TR or ATR tubes. A rudi¬
mentary system using a two-wire transmission line is shown in Fig. IT 14.
The high-power pulse from the magnetron breaks down the gap in the
ATR tube and the pow'er flows out toward the antenna. The gap in the
TR tube in the receiving branch likewise breaks down, and if it is designed
so that the discharge takes negligible power to maintain, puts a short
circuit across the line to the receiver. The delicate input circuits of the
receiver are thereby protected. Since the short circuit is a quarter wave¬
length from the T-junction, the impedance put in parallel with the
antenna line at the junction is very high and does not affect the w r ave
traveling toward the antenna. At the end of the transmitted pulse, the
discharge across the gaps goes out and the system is ready to receive echo
signals. The impedance at the T-junction looking toward the magnetron
is infinite because there is an open circuit half a wavelength away.

1 Microwave Duplexers , Vol. 14.

Fig. 11-14.—Duplexing system on two-wire
transmission line.

408

R-F COMPONENTS

[Sec. 11-5

Looking toward the receiver, there is a matched line. All the power
goes into the receiver.

In one variation of the basic scheme just outlined, the receiver branch
joins the antenna line in a series rather than in a shunt T. Then the TR
switch must be a half wavelength rather than a quarter wavelength from
the junction. In another variation, advantage is taken of the fact that
the cold (i.e., non oscillating) impedance of certain types of magnetrons is
such as to be a bad mismatch to the line, so that nearly all the power
coming toward the magnetron is reflected. Then the ATR switch can
be omitted if the line length between the magnetron and T-junction is
chosen correctly. This is known as “pre-plumbing.” With many types
of magnetron it is not feasible.

The requirements for satisfactory transmission of the outgoing pulse
are rather easily met.

1. The loss in the discharge across the gaps must be a small fraction
of the magnetron power.

2. The line must be matched when the gaps are fired.

From the point of view of the receiver, the requirements are much
more stringent.

1. During the transmitted pulse, the power getting past the TR
switch into the receiver must be less than 0.1 watt or the crystal
may be damaged. This means a minimum attenuation of 60 to
70 db.

2. The TR-tube gap must fire in less than 0.01 ^sec, or the preigni¬
tion “spike” of magnetron energy may burn out the crystal.

3. The gap must deionize in a few microseconds at the end of the mag¬
netron pulse so that echoes from nearby objects will not be unduly
attenuated. A typical specification would demand less than 3-db
attenuation 6 p sec after the pulse.

4. The received signal must see a reasonably good match into the
receiver, and the losses must be kept to a minimum.

Some refinements in the rudimentary system of Fig. 11T4 are neces¬
sary to meet the above requirements. The fired TR-tube gap is not a
perfect short circuit. If the voltage across the arc is V, the leakage power
going to the receiver is V 1 /Z, where Z is the impedance looking toward
the receiver, measured at the gap terminals. The voltage can be made
smaller by having the discharge take place in a gas at a pressure of only a
few millimeters of mercury. Further reduction of leakage power is
necessary, however. This may be done by a step-up transformer to the
gap, and an identical step-down transformer to the receiver line. In the
unfired condition, the standard line impedance is maintained on either
side of the TR switch, but in the fired condition the line impedance seen
at the gap appears to be very high and much less power is coupled out
to the receiver.

Sec. 11-61

DUPLEXING AND TR SWITCHES

409

The practical method of accomplishing this impedance transformation
is by means of a resonant cavity. Figure 11T5 shows a section through
a 1B27 TR tube and associated cavity, with input and output couplings.
The gap across which the discharge takes place is formed by two reentrant
cones on the axis of symmetry of the approximately cylindrical cavity.
The cones add capacity to the resonant circuit and the cavity is smaller
for the same wavelength than it would be without them. Tuning is
accomplished by pushing one cone in and out on a flexible diaphragm.
The unloaded Q of the cavity is lower than that of a cylinder because of

From T-junction Flexible

Fig. 11*15.—1B27 TR tube and cavity assembly with loop coupling.

the presence of the cones and the glass of the gas enclosure; it is about
2000. With normal input and output loading, the loaded Q is about 350.
Both input and output coaxial lines end in coupling loops w r hich play the
role of the step-up and step-down transformers. They can be thought
of as single-turn windings which, in proportion to their area, loop more
or less of the magnetic field existing in the cavity. The smaller the loop,
the higher the step-up ratio and the higher the loaded Q.

As a result of the impedance transformation, the arc coupling (i.e.,
the power going to the receiver as a result of the voltage across the arc
discharge) is well below the danger point and is independent of input
power. There is a second mechanism of coupling, called direct coupling,
which gives leakage power proportional to input power. At the higher
transmitter pow r ers, direct coupling becomes more important as a source
of leakage power than arc coupling. Direct-coupling power is the power

410

R-F COMPONENTS

[Sec. 11-5

that would be coupled from loop to loop with a solid metal post in the

center of the cavity, the annular
beyond cutoff.

To insure rapid breakdown at
the beginning of each pulse, a sup¬
ply of ions in the gap is maintained
by a continuous auxiliary dis¬
charge inside one of the cones.
This requires an extra electrode,
known as the “keep-alive” elec¬
trode, which draws about 150
from an 800-volt supply. A bal¬
last resistor drops the voltage to
about 400 volts at the electrode
itself. Despite this precaution,
the leakage power through a TR
tube shows an initial spike (Fig.
11-16) which precedes the “flat”
region of constant leakage power.

For rapid deionization of the
gap one constituent of the gas must
have an electron affinity. After
the discharge is over, in the absence

Time-*- |*-Pulse width 1 /isec-*j

Fio. 11*16.—TR leakage power during
a l-/isec pulse.

space around it being a waveguide

of a strong field, electrons are quickly removed by attachment to molecules.
Molecular ions have so much inertia that at the frequencies involved
they cause negligible attenuation. Water vapor is the constituent
usually introduced to hurry the electron cleanup. A typical filling would
be hydrogen at a pressure of 10 mm of mercury, and water vapor likewise
at 10-mm pressure. The hydrogen gives protection if the water vapor is
frozen out, but deionization will then be slow. Argon is used in some
tubes instead of hydrogen.

The loss to the received signal in passing through an unfired TR tube
is from 1.0 to 1.5 db, occurring mainly in the walls of the cavity.

Sec. 11-5]

DUPLEXING AND TR SWITCHES

411

Figure 11-17 shows a cut-away view of another type of TR tube, the
1B24, which is widely used in the 3-cm band. It is of the integral-cavity
type—that is, all of the cavity contains gas, not just the central portion.
A gas reservoir on the side increases the total volume of gas over that
contained in the relatively small 3-cm cavity. The tube is clamped
between standard 3-cm rectangular choke joints, and coupling into and
out of the cavity is by means of round windows or irises. Glass is
soldered across them to seal the gas enclosure. Such windows play the
same role in coupling cavities to waveguide as do coupling loops for
coaxial line. On 10-cm systems using
waveguide, the input coupling may be
by means of an iris, and the output by
a coupling loop.

Switches exactly like TR switches
with the output coupling omitted may
be used as ATR switches. However,
since the double adjustment of the two
switches is not always made correctly,
fixed-tuned, low-Q ATR switches are
preferable. Figure 11-18 shows the
1B35 tube, designed for the 3-cm band,
and its mounting. One such tube will
cover a frequency band of 3 per cent,
and pairs of these tubes will cover a
band of 6 per cent. The loaded Q of
the cavity is made very low (approxi¬
mately 5) by a large window in the end. ria - n ' 18 'T 1B35 b ™ adba " d atr tube
The cavity is placed in senes with the

magnetron line by simply substituting the face of the tube containing the
window for a portion of the broad side of the waveguide. The breakdown
takes place across the inner face of the elongated glass window.

A duplexer that represents in waveguide the basic scheme of Fig.
11-14 appears in Fig. 11-29 as part of an r-f transmitting and receiving
system. The TR-tube input window is in contact with the narrow side
of the waveguide. From the resemblance of a waveguide to a stub-
supported two-wire transmission line, illustrated in Fig. 11-8, it is
apparent that a T-junction on the narrow side of the guide is a parallel
connection, and that the plane of the narrow side is a quarter wavelength
from the effective center of the waveguide circuit.

MICROWAVE COMPONENTS OF THE RECEIVER

After emerging from the TR switch, the received signal is mixed with
the local-oscillator signal and the combination applied to the crystal, in

412

R-F COMPONENTS

[Sec. 11-6

order to obtain a much lower beat frequency which can be amplified.
A more complete and integrated discussion of microwave receivers is
reserved for the next chapter, but for the sake of continuity the compo¬
nents of the receiver which handle microwaves are treated here in con¬
junction with other r-f components.

11*6. The Mixer Crystal. —Since no satisfactory amplifier for micro-
waves exists, the conversion to intermediate frequency must be made at

the low level of received signal powers. It is important, therefore, that
the nonlinear element be as efficient as possible, and that a minimum
amount of added noise be introduced. The most satisfactory device
that has been found is the rectifying contact between a metallic point
and a crystal of silicon. 1 For protection and stability the silicon and the
“cat whisker’’ are sealed up in a cartridge. The term “crystal” ordi¬
narily refers to the whole assembly, a cross-section view of which is
shown in Fig. 11T9.

The d-c characteristic of a crystal has the form shown in Fig. 11-20.
An equivalent circuit that accounts for the r-f properties is shown in
Fig. 11-21. The nonlinear resistance of the rectifying contact is denoted
by r c . In parallel with it is the capacity C of the boundary layer of the

1 Crystal Rectifiers, Vol. 15. Radiation Laboratory Series.

Sec. 11-61

THE MIXER CRYSTAL

413

semiconductor. At sufficiently high frequencies, the capacity will short-
circuit the high back-resistance of r c and reduce the rectification efficiency.
In series with this combination is R, the so-called “spreading resistance,”
representing the bulk resistance of the silicon. Analysis shows that RC
must be small compared with the time of one r-f cycle for efficient recti¬
fication. The effects of R and C can be minimized by small contact
area, and it is possible to make crystals with nearly as good conversion

Applied voltage in volts

efficiency as would be obtained from
a simple diode at much lower fre¬
quencies. The conversion loss, de¬
fined as ratio of r-f signal power to i-f
signal power, runs from 5 to 8 db for
typical microwave crystals.

Fio. 11-20.—Typical characteristic curve of Fig. 11-21.—Equivalent circuit

a silicon rectifier. of a crystal rectifier.

Experimentally it is found that in the presence of local-oscillator
power flowing through it, a crystal generates more noise power than would
an equivalent resistor at that temperature. As a measure of this prop¬
erty, a crystal is assigned a “noise temperature,” defined as the ratio of
the absolute temperature at which an equivalent resistor would generate
the observed noise to the actual temperature. Noise temperatures
between 1.1 and 3.0 are typical. The noise generated by the crystal
increases with local-oscillator input. There is a rather broad region of
best over-all performance at 0.5 to 1.0 mw input which is a compromise
between increasing noise at high inputs and greater conversion loss at
low inputs. This optimum input corresponds to the widely used standard
operating point of 0.5-ma d-c crystal current.

The contact area between the whisker and the silicon is of the order
of 10 -6 cm 2 . Relatively low currents, therefore, yield high current
densities, with attendant local heating and danger of burnout. For
continuously applied power the danger line is of the order of a watt; this
would apply to the flat part of the TR-tube leakage. The initial pre¬
ignition spike (Fig. 11-16) is so short (less than 0.01 Msec) that the heat
cannot be conducted away from the contact; consequently the total spike
energy rather than the peak power is the important quantity. Experi¬
ence has shown that burnout is far more likely to come from the spike
than from the flat. Since TR-tube conditions are difficult to reproduce,

414

R-F COMPONENTS

[Sec. 11-7

crystals are tested by sending through them a d-c pulse of duration
2.5 X 10 -9 sec and total energy of the order of an erg. Crystals which
pass this test are safe in a properly operating radar set.

Table 11-2 lists for comparison the rejection-limit specifications of the
most widely used crystals in the three radar bands. The bearing of these
figures on the over-all sensitivity limit of microwave receivers is discussed
in Chap. 12.

In the manufacture of crystals to meet the specifications (which are a
considerable advance over those met by the crystals used in early micro-
wave radars) careful attention must be given to the original purity of the
silicon, to “doping” with small amounts of the proper impurity, to the
preparation of the crystal face, and to the sharpening and adjustment of
the whisker. Crystals are stored in metal containers to avoid burnout
from stray r-f fields. They can be burned out easily at the time of instal¬
lation by an accidental discharge of static electricity through them.

Table 11-2.— Specifications of Converter-type Crystals

Type

Wavelength
band (cm)

Conversion
loss (db)

Noise tempera¬
ture (times)

Burnout

test (ergs)

1N21B

8-11

6.5

2.0

1N23B

3.1-3.5

6.5

2.7

0.3

1N26

1.25

8.5

2.5

0.1

11-7. The Local Oscillator.—Reflex klystrons are, with very few
exceptions, used as local oscillators 1 in microwave receivers. Figure
1T22 shows a schematic view of a typical tube. The resonant circuit is a
reentrant, doughnut-like cavity
with grids across the central portion.

An electron gun with a proper focus¬
ing electrode directs a stream of
electrons through the grids. Upon
arrival at the first grid the electrons
have a velocity corresponding to 300
volts. It will be assumed that oscil¬
lations exist in the cavity. Elec¬
trons will then alternately be
accelerated and decelerated by the
r-f field across the grids. An elec¬
tron that goes through just as the
field between the grids is passing
through zero on the way from acceleration to deceleration will not have its
velocity changed and can be taken as a reference electron. In the space
1 Klystrons and Microwave Triodes, Vol. 7, Radiation Laboratory Series.

Fig. 11-22. —Schematic of reflex klystron.
H = heater
K = cathode
F = focusing electrode
C = cavity
R = reflector
0 = coaxial output line.

Sec. 11-7]

THE LOCAL OSCILLATOR

415

just beyond the grids there is a strong retarding field produced by a
reflector electrode maintained about 100 volts negative with respect to
the cathode. The trajectory of the reference electron in this space is
similar to that of a ball thrown into the air. It will return to the grids
after a time proportional to its initial velocity and inversely proportional
to the retarding field. An electron that leaves the grids earlier than the
reference electron will have been accelerated by the r-f voltage across
the cavity and, because of its higher velocity, will spend a greater time in
the reflection space. By proper adjustment of the retarding field, thedelay
may be made to compensate for its

-20

-60

-30 -40 -50

Reflector voltage

Fig. 11-23.—Reflector characteristics of the
707A.

earlier departure, and it may be
made to arrive back at the grids at
the same time as the reference
electron. Similarly, an electron
leaving later than the reference
electron catches up by spending less
time in the retarding field as a re¬
sult of its lowered velocity. The
net effect is that the electrons gather
in a bunch. 1 At certain reflector
voltages the bunch will pass through
the cavity grids in such a phase that
the r-f field retards the electrons. The electrons then give energy to the
cavity and thereby sustain the oscillations. Oscillation is observed for
more than one reflector voltage because drift times differing by a whole
r-f cycle still produce satisfactory bunching.

The net energy given to the electrons during their first passage through
the cavity is negligible when averaged over a whole cycle, being balanced
between acceleration and deceleration. On the return passage, however,
most of the electrons go through in a bunch at the most favorable phase
to aid the oscillation. Half a cycle later, when returning electrons
would absorb energy in being accelerated, very few electrons are passing
through. Useful power is delivered to an external load through a coaxial
line, loop-coupled to the cavity. The efficiency is rather low, in the
neighborhood of 1 per cent. Power outputs of 20 to 50 mw are typical.

Local oscillators are tuned by mechanically changing the size of the
cavity. A limited amount of electrical tuning is possible through varia¬
tions of the reflector voltage. Figure 11-23 shows the frequency and
power output of a 10-cm reflex klystron as a function of reflector voltage.
When the reflector is made more negative, the bunch arrives at the cavity

1 In the older two-cavity klystrons, where the bunching takes place in a field-free
space, the bunch forms about the electron that passes through the first cavity as the
field is changing from deceleration to acceleration.

416

R-F COMPONENTS

[Sec. 11-8

early, hurries the oscillation and increases the frequency. Reflector-
voltage tuning ranges of 30 to 50 Mc/sec between the half-power points
are normal, and the tuning rate may lie between 1 and 4 Mc/sec per volt.
Electrical tuning is the basis of automatic-frequency-control systems.

Fio. 11-24.—2K25 reflex klystron; 3-cm band: (a) exterior view; (6) x-ray view.

Figure 11-24 shows an exterior and an x-ray view of a 2K25, a widely
used local oscillator for the 3-cm band. The coaxial output line ends in a
probe which is inserted in the waveguide to form a matched transition
like that shown in Fig. 11- 12a.

11-8. The Mixer. —The mixer 1 contains the crystal. It has two sets
of input terminals, one for the received signal and one for the local oscil¬
lator; the output signal goes to the first stage of the i-f amplifier. The
requirements to be met are as follows: (1) the crystal must be made to
appear as a matched load to the incoming signal; (2) there must be
1 Microwave Mixers, Vol. 16, Radiation Laboratory Series.

Sec. 11-8]

THE MIXER

417

minimum loss of incoming signal into the local-oscillator input; (3) the
local oscillator must see a fairly good match, though the requirements are
not as strict as for a magnetron.

Figure 11-25 shows a coaxial-type mixer which is widely used for the
9- to 11-cm band. It bolts directly on the TR-tube cavity and the output

Fig. 11-25.—Coaxial-type mixer; 10-cm band.

coupling loop is integral with the mixer. The crystal is mounted as a
part of the center conductor of a short coaxial line and makes a matched
termination with no special transformers. Since the i-f signal must be
extracted, the end of the r-f line cannot be a d-c short circuit. An effec¬
tive r-f short circuit, with no metallic contact between inner and outer
conductor, is provided by two concentric quarter-wave sections which
form a choke not unlike that in a rotary joint. The i-f output fitting
unscrews to permit replacement of crystals.

Local-oscillator power is introduced through a side arm. About 50
mw is available from reflex klystrons in the 10-cm region, which is 20 db

418

R-F COMPONENTS

[Sec. 11-9

above the 0.5 mw needed to produce the standard 0.5 ma of crystal cur¬
rent. The great excess of power permits loose capacitive coupling
between local oscillator and crystal. By the reciprocity principle, since
there is poor transfer of power from the local-oscillator input to the signal
line, there will be poor transfer from the signal line to the local-oscillator
branch, thus satisfying the second condition stated above. 1 A screw
on a quarter-wave stub support adjusts the proximity of the capacitive
probe to the signal line and provides the method of setting the crystal
current. This is the sole adjustment.

The local-oscillator input fitting contains a resistor disk which ter¬
minates the 50-ohm cable. Since the probe is half a wavelength away
from the disk, the load at the probe will be in parallel with the disk
(Sec. Il l); but since the probe does not differ much from an open circuit,
the load for the local oscillator is still a good match. The voltage at the
probe is the same as that at the disk. It is necessary to have the probe
spaced a quarter wavelength on the signal line from the effective plane
of the coupling loop. With a loaded Q of 350 the TR tube is considerably
off-tune at the local-oscillator frequency, which is usually 30 Mc/sec
away from the signal frequency. Like all parallel resonant circuits, the
TR cavity presents a very low impedance, practically a short circuit, at
frequencies off resonance. If the probe were half a wavelength from the
coupling loop, it would be effectively at a short-circuit point for local-
oscillator frequency and no power could be transferred. At a quarter-
wave point the short circuit at the coupling loop is reflected as an open
circuit and the piece of line is, to the local-oscillator frequency, a stub
support.

In mixers for the 3-cm region, the crystal goes directly across the
center of the guide. Coupling between local-oscillator waveguide and
crystal guide is by means of adjustable windows in the short face of the
guide. At 10 cm coaxial cables carry the local-oscillator power to sepa¬
rate radar and AFC mixers, but at 3 cm double mixers are used in which
the two crystals are on opposite sides of the local oscillator. Figure 11-29
shows a waveguide mixer and other r-f components for the 3-cm band
with AFC and beacon features.

11-9. Automatic Frequency Control. —Radar automatic frequency
control (AFC) is a scheme in which the difference in frequency between
the magnetron and the local oscillator is compared in a discriminator cir-

1 In an exact calculation, account must be taken of the difference in the impedance
of the various branches at signal and local-oscillator frequencies. As is mentioned
in the next paragraph, this is considerable for the highly resonant TR cavity. Quali¬
tatively, however, the reciprocity argument is valid. The so-called “magic T” pro¬
vides a method of decoupling the signal and local-oscillator inputs that does not
depend on an excess of local-oscillator power. See Microwave Mixers, Vol. 16,
Chap. 6.

Sec. 1110 ]

REASONS FOR AN R-F PACKAGE

419

cuit with the standard intermediate frequency being used—for example,
30 Mc/sec. An error in the difference frequency produces a voltage that
is applied to the reflector of the local oscillator in such a sense as to bring
the local oscillator into correct tune. Because of the close connection
of the whole AFC problem with receiver design, consideration of this
subject is deferred to Sec. 12-7.

MOUNTING THE R-F PARTS

Experience has demonstrated that good radar performance depends
not only on a well-designed set of microwave components but also on a
properly coordinated mounting of them, relative to each other and rela¬
tive to the other parts of the radar. Therefore it is necessary to add to
the treatment already given of the components themselves a considera¬
tion of the engineering reasons for the accepted practice of grouping
certain vital components in a major unit called the “r-f head.”

11-10. Reasons for an R-f Package. Preferred Grouping of Com¬
ponents .—Considerations of accessibility and convenience would often
argue for putting most of the components of a radar set near the indicator
rather than near the antenna, which, in order to get the proper view,
must usually be at a remote or isolated point. However, the long-line
effect discussed in Sec. Il l makes a long transmission line from magne¬
tron to antenna something to be avoided if possible. In addition to the
fact that in a long line even a moderately low standing-wave ratio can
cause instability in the magnetron, the extra junctions, bends, and elbows
needed for a long line are themselves likely to add to the mismatch.
Furthermore, as seen from Table 11-1, the r-f attenuation in a long line,
particularly at the higher microwave frequencies, results in the loss of
several decibels when two-way transmission is considered.

The shortest possible r-f line is realized by mounting the magnetron
on the back of the antenna reflector (“back-of-the-dish system”). This
ideal arrangement is often not practical because of a group of components
functionally associated with the magnetron which may be too large and
heavy for the antenna mount to carry. The pulse transformer must be
adjacent to the magnetron to avoid long high-voltage leads, which would
have to be supported and properly insulated and would add unwanted
capacity. The duplexer T-junction and the TR tube must, of course,
go in the magnetron-antenna line. The extremely low-level echo signals
coming through the TR tube must be converted to the intermediate
frequency and amplified considerably before being transmitted to a
remote point. The local oscillator must be close, because the AFC is
based on a comparison of the frequency of the local oscillator and that of
the magnetron.

Electrical and functional considerations dictate, then, that the follow-

R-F COMPONENTS

420

[Sec. 11-10

ing minimum items be mounted in a group and that the group be as near
the antenna as practical:

1. Pulse transformer.

2. Magnetron.

3. Duplexer, TR and ATR tubes.

4. Local oscillator.

5. Radar and AFC mixer.

6. AFC control circuits.

7. I-f amplifier (usually up to 1-volt video level).

This set of components, mounted as a group and usually in a closed
container, is called the “R-f Head.” Alternative terms are “R-f Unit”
and “Transmit-receive Unit.” Beacon local oscillator and beacon AFC
are included where beacon reception is required. In smaller radar sets,
the modulator network and switch tube and even the modulator power
supply may be put with the r-f unit. An extension of this trend leads to
an arrangement with all parts of the radar except the controls and the
indicator tube in a single container.

Advantages of an R-f Package .—On all but the largest radar sets the
group of components listed in the previous paragraph can be compactly
mounted in a single container that is not too heavy for one man, or at
most two men, to carry. There is considerable advantage in having the
vital parts of the transmitter and receiver centralized in a demountable
unit package. In the event of trouble, a spare r-f head can be substituted
and connected into the rest of the radar in a few minutes. Diagnosis of
trouble, repair, and readjustment, as well as assessment of performance,
can all be performed on a well-equipped test bench. This is particularly
helpful for airborne sets.

Good engineering practice favors pressurization of the r-f transmission
lines of microwave radar systems in order to keep out water and water
vapor. For high-altitude operation, pressurization may be absolutely
necessary to prevent breakdown of the line. The high-voltage cathode
circuit of the magnetron is a similar case. Pressurization assures dry
conditions and sea-level pressure, and thus makes unnecessary the huge
insulators and large air clearances that standard engineering practice
would otherwise prescribe. Other parts of the r-f head can be made
smaller and more compact if pressurized conditions are assumed. It is
but a slight extension to consider that the r-f head should go into a single
pressurized container, with the pressure common to the r-f line out to the
antenna. Such a plan solves two other problems: (1) the working parts
of the r-f head are protected against the most severe conditions of
moisture, salt spray, and dust, not only in use, but also during shipment
and storage; and (2) the shielding problem is greatly simplified, both for
keeping external disturbances out of the delicate parts of the receiver, and

Sec. 1111] DESIGN CONSIDERATIONS FOR THE R-F HEAD

421

for confining the disturbances set up by the radar transmitter so that
they do not affect other equipment.

11-11. Design Considerations for the R-f Head. —The form which
the r-f head takes will depend on whether it operates on the ground, on a
ship, or in an airplane; on the degree of exposure to the elements; and on
the power and transmitting frequency of the magnetron. Pressurization
has advantages and disadvantages. Among the latter are inconvenience
resulting from inaccessibility of parts for adjustment and repair, and
difficulty of transferring heat through the pressure wall. The r-f head
of a small airborne set will undoubtedly be a completely pressurized unit.
The r-f head of a very large ground set might operate inside a protective
housing and not be pressurized at all. Between these two extreme types
are designs where part is pressurized and part is not. No firm rules can
be laid down. The treatment here will outline the conditions that must
be met, and then give illustrative examples of two quite different designs.

Heat Removal . 1 —The maximum safe ambient temperature for most
of the r-f-head components—such as composition resistors, oil-paper
condensers, and blower motors—is about 85°C. The temperature of the
air around the r-f head may get as high as 50°C in desert areas inside a
housing exposed to the sun’s rays. If the unit is not pressurized the per¬
mitted differential of 35°C is easily met. The air from a simple blower,
properly channeled, will readily carry the heat released inside the enclos¬
ure out into the surrounding air. Often the air from the magnetron
cooling blower can be so directed as to do what additional cooling is
needed. Subunits tightly enclosed for reasons of electrical shielding may,
however, need additional circulation.

Where the free flow of external air through the r-f head is blocked off,
as it must be by a pressure housing, the problem of transferring the heat
to the outside air can easily be a limiting factor in design. The difficulty
is not in getting the heat through the actual metal wall. A short com¬
putation shows that a differential of a fraction of a degree is sufficient for
this. Almost all of the temperature drop occurs across the dead-air
films on the two sides of the wall. Natural convection results in a
transfer coefficient of only 0.006 to 0.010 watts/in 2 per °C difference in
temperature between the air and the wall. If 30°C be taken as a safe
figure for rise of internal air over external air, and if natural convection
be assumed on both sides, then the average coefficient given above would
result in a maximum thermal load of 0.12 watts/in 2 . Forced convection
from a gentle current of air along the surface raises the coefficient to 0.02
watts/in 2 per °C, but beyond this increased velocity results in only a slow
increase. A high-velocity flow of perhaps 50 ft/sec is necessary to
achieve a figure of 0.04 watts/in 2 per °C.

1 Amer. Soc. of Heating and Ventilating Engineers Handbook.

422

R-F COMPONENTS

[Sec. 1111

The increase in the coefficient is due mainly to creating a turbulent
layer where good mixing occurs close to the actual wall, and to reducing
the thickness of the poorly conducting layer. The cooling blast for a
magnetron approximates the necessary conditions, but maintenance of
turbulent flow over large areas takes considerable power.

The conclusion is that with moderate blowing on the inside and
natural convection outside, the loading can increase to 0.17 watts/in 2 ,
and with blowing on both sides can increase to 0.3 watts/in 2 , for an over-

'n r

Fio. 11-26.—Methods of improving heat transfer through pressurized containers.

all rise of 30°C in air temperature. These figures are all approximate,
since the geometry is never simple and uniform conditions of air flow
over a whole vessel are never realized.

Radiation plays a minor role in heat transfer for the differentials here
involved. Painted rather than bright surfaces are worth while, however.
Fins are helpful in increasing effective area, especially with natural con¬
vection, though not in proportion to actual surface. If the forced con¬
vection is not along the fins they do not help at all, because the increased
area is compensated by impediment to air flow.

Two schemes to improve heat transfer are shown in Fig. 11-26. In
o, the internal and external blowers are directed at the same portion of
the wall, which has some fins at that point at least to increase effective
area. In the region of turbulent flow directly under the blower output
the transfer coefficient is high. In the second case, b, there is an outer
shell close to the wall of the pressure container. A powerful blower
maintains turbulent flow over the whole interspace and a high coefficient
results. This may be repeated on the inner wall of the pressure housing.

Sec. 1111] DESIGN CONSIDERATIONS FOR THE R-F HEAD

423

Types of Container .—If the r-f head is not pressurized, the supporting
framework for the parts will be a rectangular affair consonant with the
standard construction practices used on the rest of the radar. The usual
rules of accessibility and convenience will dictate the placement of parts.
If, however, the unit is to be pressurized, further consideration must be
given to the container. It is almost essential to be able to remove the
pressure cover and make tests and adjustments without disconnecting
the r-f transmission line or any power or signal cable. This rules out
methods of mounting the units in which the support brackets attach
to the pressure cover.

Fig. 11-27.—Exterior view of a 3-cin airborne r-f head.

Although rectangular containers are most economical of space, they
are difficult to pressurize because of their tendency to become spherical
under pressure, with resultant severe shear strains in the corners. In a
ship set, where only small pressure differentials are expected, a rectangular
cover is feasible. If it is not too large, a rectangular housing cast out of
light metal can be made strong enough to stand the 30 lb/in 2 test pressure
required for airborne r-f heads. It has been common practice, however,
to use cylindrical housings with domed ends because only tensile strains
are then involved and the housing can be very light.

One example of pressurized airborne container design is illustrated
in Fig. 11-27, and discussed fully in See. 11-12.

The heat generated in the magnetron rises as the average power level
is increased, but the generation of heat in the receiver components is
substantially constant from one radar set to another. If the transmitter
power is more than about 50 kw, the thermal load for any pressurized

424

R-F COMPONENTS

[Sec. 11-11

container of reasonable size would be above the limit set in Sec. 11-11.
Under these circumstances, it is customary to mount the magnetron
anode and the pulse transformer case outside the pressurized shell, with
an external blower to cool them. The cathode connection to the magne¬
tron is made in a pressurized inner compartment, into which gasketed
bushings bring the pulse transformer output and the magnetron cathode
leads. The waveguide r-f line is pressurized from the magnetron output
to the pressurized compartment which houses the duplexer, as well as on
the antenna side. In this arrangement, high voltages appear only inside
pressurized spaces, while most of the heat is liberated in the open, where
it can be carried away by the air stream from the external blower.

Metering and Test Points .—Good radar performance depends on
objective tests of the functioning of each part. The vital radar com¬
ponents are all centralized in the r-f head, and the providing of necessary
test points there is a part of the design job. Testing should not require
removal of any covers. A directional coupler, used to introduce the test
signal, will be located on the antenna line either just outside the r-f head
or just inside with cable feed to a test jack on the outside wall. At the
higher microwave frequencies, cables and cable fittings introduce a vari¬
able element and the external location would be preferred. The video
output jack required can be the normal output to the indicator, in which
case an interchange of cable is required. If the video output tube is
capable of handling parallel loads, a second jack for test purposes only
would be added. If the test set requires a trigger signal at the time of
the magnetron pulse, this can be obtained by inserting a few ohms in the
bypass-to-ground circuit at the low end of the pulse transformer. The
signal would go in a shielded cable to an appropriate external jack.

The other checks on the operation of the r-f head divide themselves
into (1) minimum information continuously available to a remote opera¬
tor and (2) tests to be performed with the cover removed.

The average magnetron current is the most important single item in
monitoring a radar set. If it has the correct value, the magnetron is
operating at the recommended point on its performance chart and is
almost certainly putting r-f power into the antenna line. Sparking
of the magnetron or irregular modulator operation can be observed.
This meter reading is an over-all check on the operation of the radar
transmitter.

The second most important item for the operator to monitor is the
radar crystal current. If this maintains its original value, it is known
that the local oscillator is functioning and the crystal has not changed its
properties. A decrease may indicate a burned-out or damaged crystal.
A rhythmical variation indicates that the AFC is searching but not
locking.

Sec. 11-12]

ILLUSTRATIVE EXAMPLES OF R-F HEADS

425

A single remote meter with a selector switch, or selector relays in the
r-f head, can perform these minimum monitoring functions at the opera¬
tor’s position. If the set has beacon AFC, the radar-beacon switching
relay should transfer the remote meter to the beacon cavity crystal.
Then a steady meter reading indicates not only that the beacon AFC is
locked, but that it is locked at the correct frequency, since the crystal
energy has come through the reference cavity.

Of the test points usually provided for cover-off checking, the most
essential is a jack to measure the crystal current at every crystal, in order
to permit adjustment of the local-oscillator coupling. On crystals
where the same current is metered remotely as well, a cut-in jack is used.
Another current worth metering is the average diode current in the second
detector, for over-all sensitivity tests and checking the receiver. A jack
for measuring the keep-alive current in the TR tube should be included
to provide verification that the TR switch is performing normally.

In radar sets where the r-f head is accessible to an operator during
operation, all of the above metering can be done on a single meter and
selector switch.

The most important internal signal test point is the AFC video output.
On an oscilloscope the discriminator output is seen, as well as any spuri¬
ous signals. Sometimes this is made a phone jack also, so that with a pair
of headphones aural indication of crossover may be compared with the
frequency of best tune.

11-12. Illustrative Examples of R-f Heads. Airborne Search Set.
Figure 11-27 shows an external view of the r-f head used on a 3-cm search
and navigation set of recent design. A broad flat container was dictated
by the space available in certain aircraft. A lightweight sheet-metal
pressure vessel of this form factor must of necessity have a domed top and
bottom. The pressure seal comes near the top of a short central cylindri¬
cal section 18 in. in diameter.

The radar set is designed to work on three pulse lengths: (1) 5 Msec,
200 pps, for search; (2) 2.5 Msec, 400 pps, for beacon interrogation; and
(3) 0.5 Msec, 800 pps for high definition. The long pulse, as shown in
Sec. 2-9, gives greater range, particularly in mapping land-water bound¬
aries. It must be longer than the upper discrimination limit of ground
beacons. The beacon pulse is well over the minimum length of 2 Msec
necessary to trigger beacons.

The pulse is transmitted from the modulator on a 50-ohm cable, which
enters the r-f head via a pressurized pulse connector fitting. The
shielded cable then goes to the quadrant-shaped pulse compartment.
Into this compartment project the pulse transformer bushings and the
magnetron cathode bushing. The interior detail is shown in Fig. 11-28.
Ordinarily the quadrant cover is on and no high voltages are exposed

42C

R-F COMPONENTS

[Sec. 11-12

when the lid of the whole r-f head is off. The pulse compartment also
contains the magnetron cathode-heating transformer and the necessary
bypass condensers to provide a pulse path to ground in the metering
circuit. All wires that leave this well-shielded compartment go through

Fig. 11-28.—Interior view of a 3-cm airborne r-f head; (a) pulse input; (b) pulse trans¬
former; (c) pulse compartment; ( d ) pulse transformer bushing; (e) magnetron cathode
bushing; (/) blower motor; (g) AFC chassis; (/i) receiver chassis; (i) beacon reference
cavity; (J) shield for local oscillators; (A;) double mixer; ( l ) TR tube.

filters which reduce pulse voltages on them to a level that will not inter¬
fere with communications. The pulse transformer case, being the
source of some heat, projects outside the airtight compartment.

The r-f system of this unit is shown in Fig. 11-29. The magnetron,
type 4J52, is of the “packaged” design; the magnet is an integral part of
the tube. It operates at an input level of about 200 kw, with an average
efficiency of about 30 per cent. Its cathode is larger than is usual for

428

R-F COMPONENTS

[Sec. 11-12

magnetrons of this power; thus the tube is better able to furnish the
long 5-Msec pulse without sparking. Its cooling blower also provides the
general air circulation inside the r-f head.

The waveguide fittings inside the r-f head are not airtight; they com¬
municate the head pressure to the antenna waveguide run. However,
electrically the waveguide is kept sealed as tightly as possible in order to
prevent the general level of leakage power in the closed container being
high enough to interfere with AFC operation. The sealing is done by
woven metal gaskets at every junction. A short section of flexible
corrugated waveguide next to the magnetron absorbs the dimensional
tolerances and permits all parts to be bolted together tightly without
strain.

The duplexer-mixer portion of the r-f system follows closely the block
diagram of Fig. 1212. The TR tube is a 1B24. Its r-f selectivity is high
enough (about 50 Mc/sec between the half-power points) so that when
tuned up for radar reception the loss in receiving beacon signals may be
as much as. 20 db. This loss is averted by a solenoid-actuated plunger
inserted in the waveguide on the low-power side of the TR tube at a
distance of half a guide-wavelength from its output window. By adjust¬
ing the depth of insertion, the TR tube can be pulled into good tune for
the new frequency.

The outputs of the radar and AFC crystals go in double-shielded
cables to the receiver and AFC chassis respectively. The AFC control
circuit is essentially of the form described in Sec. 12-7. For best use of
the available space, the receiver chassis is in the form of a segment of a
circle. The normal chain of i-f amplifier stages, second detector, and
video output stage, is arranged around the periphery. The bandwidth of
the i-f amplifier is 5 Mc/sec, but for long-pulse operation a relay switches
the bandwidth to 1.0 Mc/sec by changing the loading of one of the inter¬
stage tuned circuits. This is necessary to realize the full gain in sensi¬
tivity to be expected from the long pulse. The bandwidth is still 5 times
the reciprocal pulse length, rather than the value of 1 to 2 times estab¬
lished as optimum in Sec. 2-9. There are two reasons for this: (1) fre¬
quency modulation of ihe magnetron owing to variations of current
during the long pulse can lead to a spectrum wider than theoretical; and
(2) it is difficult to make a practical AFC that will hold a set in tune to a
small fraction of a megacycle per second.

No d-c power supplies are provided in the r-f head, except for the TR-
tube keep-alive supply. This is a small half-wave supply with resistance-
capacity filter, located under the receiver chassis. All other voltages for
the local oscillators, receiver, and AFC come in over wires in the large
cable connector from an external centralized supply.

The various subunits in the r-f head are designed with plug connec-

Sec. 1112)

ILLUSTRATIVE EXAMPLES OF R-F HEADS

429

tions so that they may be quickly removed for servicing or replacement
with spare units. Remote metering of magnetron current, radar crystal
current, and beacon cavity crystal current is provided.

Shipborne Air-search Set .—The final example is the r-f unit of a
high-power shipborne set for maintaining air surveillance. The r-f head

Fig. 11-30.—Front view of r-f head, shipborne radar: (a) pulse input; (6) transmitter
compartment, search radar; (c) receiver, search radar; (d) ATR mount; (e) AFC mixer;
(/) radar mixer; (g) TR-tube mount; ( h ) r-f switch for noise source; (i) receiver, height-
finder radar; (j) duplexer, height-finder radar; ( k,l ) built-in control and test equipment.

illustrates many points of good design applicable to high-power sets in
the 10-cm region whether shipborne or not. Figure 1T30 shows a front
view of the r-f head.

This equipment is a dual set with separate radars on different
frequencies, one for long-range search and one for height-finding. The
two antennas are mounted on a turret about 5 ft in diameter which con¬
tains the r-f head and has room for an operator during tests The

430

R-F COMPONENTS

[Sec. 1112

arrangement is therefore a back-of-dish mounting with short waveguide
runs to the antenna, as was recommended in Sec. 11-10. The pulses
from the two modulators are transmitted through rotary joints. All

Fig. 11-31.—Transmitter compartment, shipborne radar: (a) magnet; (b) “doorknob”
transition; (c) magnetron cathode bushing; (<2) despiking resistor; (e) pulse-transformer out¬
put bushing; (/) pulse transformer case, directional coupler of opposite transmitter in
front.

other power, signal, and control connections to the rotating turret are
made via slip rings.

Each of the end compartments contains the transmitter components

Sec. 1112]

ILLUSTRATIVE EXAMPLES Of R-F HEADS

431

of one of the radars. Figure 11 -31 shows the interior detail of one of these
compartments; in the other, the items are the same but are mounted the
other end up. The pulse from the modulator comes in through the pulse
connector on the end of the case. For the long-range search set the
power from the modulator is about 2 Mw, or about 10 kv on the 50-ohm
cable. This power goes in parallel to the primary of the pulse transformer
and to a despiking network consisting of a 50-ohm resistor and a 400-MMf
condenser in series to ground. The network provides a transient load
for the modulator while the voltage is rising but before the magnetron
starts to draw current.

On the long-range search set, a 4J32 magnetron furnishes 0.8 Mw of
r-f power. The pulse length is 1 ^tsec and the repetition rate is 390 pps.
Since the peak voltage at the cathode is about 28 kv, good clearance must
be maintained. The magnetron output is in lf-in. OD coaxial line, but
an immediate transition is made to standard waveguide l£ by 3 in. with
0.080-in. wall. Since both the coaxial line and waveguide are operating
not very far from the voltage-breakdown point, a specially tapered “door¬
knob” transition is necessary. A small air gap in the choke-flange
coupling between the transition section and the waveguide outlet absorbs
the tolerances in the magnetron mounting. The whole magnetron high-
voltage compartment is tightly closed in operation. The small upper
compartment is mainly taken up with the fluted case of the pulse trans¬
former. The antenna waveguide of the other radar goes through in
front and the directional coupler is put in this convenient place.

In the central section are the two duplexer sections and the two
receivers. The duplexer section for the search radar stretches across the
lower part of the case. Nearest the magnetron is the AFC attenuator
and mixer. The mixer is of the type shown in Fig. 11-25, Sec. 11-8. One
coaxial cable brings r-f power from the local oscillator, which is mounted
in a well-shielded compartment in the receiver box. The other carries
the i-f signal to the AFC discriminator and control circuit in the same box.

Next along the guide and on the opposite side are the two ATR tubes,
of the untuned low-Q type, spaced one half of a guide wavelength apart.
This gives a broadband characteristic. 1 The resonant windows are
made a part of the broad face of the waveguide. A half wavelength
farther down the guide, and on the same side as the AFC attenuator, is
found the duplexer T. The TR cavity is iris-coupled, both on the input
side from the end of the waveguide and on the output to a coaxial mixer
which is otherwise the same as the AFC mixer. As in the AFC case, i-f
cables connect the mixer with the local oscillator and the proper parts
of the receiver.

The last part of the duplexer section is an r-f switch used in testing

1 Microwave Duplexers, Vol. 14.

432

R-F COMPONENTS

[Sec. 11-12

the receiver sensitivity. In the radar operating position a straight piece
of waveguide with a choke-flange joint at each end transmits the power
direct to the antenna. There is, of course, appreciable r-f leakage at the
air gaps of the two junctions. Accurate construction keeps this small
enough not to affect the AFC mixer in the same compartment. A safety
switch prevents turning on the magnetron unless the guide is in proper
position. This piece slides out of the way and a matched probe-fed
transition piece slides in for introducing a test signal.

The receivers are typical of ground and ship sets, except that in this
case they do not contain the regulated power supplies. The usual i-f and
video amplifier, the various anticlutter circuits, and the AFC circuits are
included. A tight outer box provides general shielding, but the i-f
amplifier and local oscillator have inner shields in addition.

One of the most noteworthy features of this radar is the built-in
test equipment. An operator can go to the turret and, by transferring
the usual remote controls to a duplicate set in the turret, operate the
radar and view the echoes or waveforms on the scope provided. A uni¬
versal meter furnishes a quick check on all the currents mentioned in
Sec. 11-11. The vital check on receiver sensitivity is made with a
klystron noise source, whose output signal is introduced via the r-f
switch just described. The reliability and day-to-day reproducibility
of the test set are excellent, and having it built in makes a quick daily
check on a continuously operated radar simple to perform. Over-all
noise figures of 9 to 12 db are commonly maintained.

Neither the r-f head nor the waveguide is pressurized. The moisture
problem in the turret is solved by electric heaters which come on when¬
ever the radar shuts down. Only a few degrees rise above general
atmosphere temperature prevents condensation. Drain holes for water
are provided at proper points in the antenna line.

CHAPTER 12

THE RECEIVING SYSTEM—RADAR RECEIVERS

By L. J. Haworth and W. H. Jordan

INTRODUCTION

By L. J. Haworth

12-1. The Role of the Receiving System. —It is the purpose of the
receiving system to extract the information contained in the radio¬
frequency echoes, to sort it in terms of the geometrical parameters
involved, and to present the results to the observer in a convenient and
useful form.

The data involved are in a variety of forms. Most of them come from
the radar set itself. First in importance, of course, are the echo signals,
which may contain as many as several million separate pieces of informa¬
tion each second. The exact instant at which the radar pulse is trans¬
mitted is known by virtue of a pulse to or from the modulator. The
geometrical coordinate of range is proportional to the return time of the
echo pulses with respect to this pulse. The orientation of the antenna is
available in terms of the rotational positions of shafts geared to the
scanner axes. These direct data are often supplemented by others
(obtained from external sources or from observation of the composite
radar results), such as geographical information, the location and orienta¬
tion of the radar platform, if it is a moving one, and so on.

Within the limitations of these data and the requirements of the par¬
ticular situation, the equipment should present to the observer a con¬
tinuous, easily understandable, geometrical picture of the radar targets
under study, giving the location, size, shape, and, in so far as possible, the
nature of each to any desired degree of accuracy. In many cases, the
equipment should have provisions for instantaneously determining in a
precise numerical way the exact position of each target with respect to
the radar set or to other targets, and often it should furnish means for
passing these results on to other devices in an automatic way. All of this
must be done in such a manner that the echo signals have optimum sen¬
sitivity compared to internal system noise and to extraneous radiations.

The accomplishment of these objectives requires a considerable array
of equipment. The ultimate link with the observer is the indicator.
The indicator proper is usually supplemented by a considerable amount

433

434

THE RECEIVING SYSTEM—RADAR RECEIVERS [Sec. 121

of auxiliary equipment, the chief functions of which are to prepare the
geometrical and other data, apart from the signals, for use by the indica¬
tor, to control the indicator functions, and to assist in the making of
measurements. No satisfactory descriptive term exists for this auxiliary
equipment, but in combination with the indicator it is known as the
“indicating (or indicator) equipment.” The echo signals must be
amplified greatly and demodulated before being presented to the indica¬
tor, usually in the form of video signals. The path which they follow in
this process will be spoken of as the “signal channel,” and the equipment
involved as the “receiver.” On some occasions the system also contains
computers or other devices which aid in the ultimate disposal of the data.

The receiver must deliver a maximum of desirable, and a minimum
of undesirable, information to the indicator. It should have as little
inherent noise as possible, since such noise determines the ultimate limit
in signal detectability. It should afford sufficient amplification to
realize this ultimate limit and sufficient dynamic range to allow wide
latitude in useful signal intensities. The bandwidth must be chosen to
provide sufficiently rapid transient response so that the details of the
signals will be preserved; but it must not be so great as to decrease unduly
the signal-to-noise discrimination. In many cases, special design char¬
acteristics enhance the discrimination of certain kinds of echo in com¬
parison to other undesired echoes or to radiations from other transmitters.

The indicating equipment, which is almost entirely responsible for
the purely geometrical aspects of the display problem, must share with
the receiver the responsibility for the discernibility of the signals with
respect to noise, interference, and signals from other targets. The indica¬
tor proper is almost always a cathode-ray tube whose screen presents the
radar display. Synthesis of such displays involves combining the signal
intelligence with antenna scanning angles and other geometrical factors
to provide an intelligible picture of the dispositions and other characteris¬
tics of the radar targets. Some of the displays are, in principle, facsimile
representations of the actual geometrical situation; others are deliberately
deformed to improve some particular type of observation or measurement.

A wide variety of displays has been discussed in Chap. 6. The basic
types are listed here for reference:

1. Deflection-modulated displays, in which the echo signals are used
to deflect the beam laterally on the tube face. In practice, the
other rectangular coordinate is invariably range (A-scope, R-scope,
etc.).

2. Intensity-modulated displays, in which the signals serve to brighten
the screen, and hence appear as bright spots or patches against a
background that is partially illuminated by the receiver noise
These fall into several categories:

Sec. 12-2]

A TYPICAL RECEIVING SYSTEM

435

a. True plots of a plane surface in which range and an angle are
combined as polar coordinates (PPI).

b. Rectangular plots of two cartesian components of range, in
general with unequal normalizations 1 (stretched PPI, RHI).

c. Rectangular plots of the polar coordinates, range and angle
(B-scope, E-scope.)

d. Rectangular plots of azimuth angle and elevation angle
(type C).

e. Modifications of the above types to indicate a third dimension
in certain simple situations.

3. Presentations, not properly displays, in which the cathode-ray
tube is used as a two-dimensional meter (spot error indicator).

Additional types of deliberate deformation of the basic displays and
certain approximations used for technical reasons will appear later in
detailed descriptions of the production of the various displays.

Observations and measurements are aided by various indices. Prac¬
tically all the displays that include range are provided with a set of pre¬
cisely timed “electronic markers” which occur at convenient regular
intervals on the display itself. These are sometimes supplemented by a
manually controlled continuously movable marker, which removes the
necessity for interpolation. Measurements of angle can be made by
means of similar electronic indices, but fixed lines etched on a transparent
overlay plus, perhaps, a movable mechanical cursor, are often used.

12-2. A Typical Receiving System. —Figure 12T illustrates the
principal parts and some of the subdivisions of a typical receiving system
containing a cathode-ray-tube indicator.

The receiver is always of the superheterodyne type and consists of the
signal channel and the local oscillator, together with frequency-control
circuits for the latter. Strictly speaking, this should include all equip¬
ment concerned with the received signal, beginning with the antenna and
ending with the input terminals of the indicator proper. However, in
practically all radar applications the antenna, the TR tube, and the r-f
line connecting them are shared with the transmission channel, and the
techniques in these sections are dictated somewhat more by the trans¬
mitter requirements than by those of the receiver. We shall, therefore,
consider the receiver as beginning at the point where the signal channel
branches from that which is shared with the transmitter.

R-f signals from the antenna by way of the TR switch enter a crystal
mixer where they are combined with the c-w output of a tuned local
oscillator to form a heterodyned signal at the desired intermediate fre¬
quency, usually 30 to 60 Mc/sec. This signal is led from the mixer into
an intermediate-frequency amplifier of very special characteristics, where

1 If the normalizations are equal the display is, of course, equivalent to Category a

THE RECEIVING SYSTEM—RADAR RECEIVERS [Sec. 12-2

Sec. 12-2]

A TYPICAL RECEIVING SYSTEM

437

it experiences an amplification of some 120 db. Following the i-f ampli¬
fier is a “second” detector and i-f filter which rectify the signals and
remove the i-f components, leaving only the video signal envelope. The
signal channel is completed by a video amplifier which delivers the
signal at proper voltage level to the input terminal of the CRT or other
indicator.

As in all superheterodynes, tuning is accomplished by controlling the
frequency of the local oscillator. Since the ratio of the bandwidth to the
carrier frequency is extremely small (of the order of one part in a few
thousand), the tuning is critical. Some form of automatic frequency
control is essential if constant manual tuning adjustments are to be
avoided. Methods of AFC in pulse radar practice are quite different
from those of radio or television; in radar, frequency control is exerted
by passing a portion of the transmitted signal through a mixer and i-f
amplifier, and maximizing its intensity by the use of a frequency dis¬
criminator and electrical circuits, which tune the local oscillator.

When the radar is to respond to beacon signals, the receiver must be
tuned to the beacon transmitter rather than to the local one. In this
case, an alternate local oscillator (not shown in Fig. 121) is forced to
oscillate in resonance with a standard cavity whose frequency differs
from that of the beacon by the intermediate frequency of the receiver.

The indicating equipment consists of the cathode-ray tube together
with the auxiliary vacuum-tube circuits and other devices necessary to
the synthesis of the display.

Those elements of the cathode-ray tube essential to a general under¬
standing are shown in Fig. 121. In addition to the screen, these consist
of a hot-cathode electron source, a “control grid” whose potential deter¬
mines the beam intensity, and a mechanism for deflecting the beam. In
the example illustrated, the deflection mechanism consists of two orthog¬
onal pairs of parallel plates between which the beam must pass, the
deflection due to each pair being proportional to the potential across it.
In another type of tube, the deflection is produced by a magnetic field
resulting from current in a coil or combination of coils surrounding the
tube “neck.” Arrangements for focusing the beam are not illustrated.

The equipment auxiliary to the cathode-ray tube varies widely with
different situations but a few general statements can be made. Those
parts concerned with the pulse-repetition cycle are collectively called the
“timer.” The timer provides synchronization with the modulator,
sweeps and markers for the display and measurement of range, blanking
of the cathode-ray tube during unused portions of the pulse cycle, and
other related operations which may arise in special cases. The remaining
equipment, apart from the necessary power supplies, is mainly concerned
with the display and measurement of geometrical quantities other than
range.

438

THE RECEIVING SYSTEM—RADAR RECEIVERS [Sec. 12-2

Since time is always measured with respect to the instant at which the
modulator fires, synchronization between the modulator and the timer is
of basic importance. In some cases, the timer exerts precise control of
exact firing time of the modulator by sending it a trigger pulse; in others,
it responds to a trigger from the modulator. In the latter case, the sys¬
tem is said to be “self-synchronous.” 1 Although certain advantages
can often be derived by giving control to the timer, this cannot always
be done, 2 and it is sometimes inconvenient in a multiple-display system.
Figure 121 illustrates a self-synchronous system. Some of the depar¬
tures possible when the timer does the synchronizing will be pointed out
in the appropriate places.

The cathode-ray tube must be turned on only during the fraction of
the pulse cycle in which it is used. One portion of the timer generates a
square wave (Waveform b, Fig. 12T) which performs this function and
usually finds other applications within the timer.

If the display includes a range sweep, as is nearly always the case, the
timer generates the waveform that ultimately produces it. This wave¬
form usually consists of a linearly increasing voltage wave which begins
at the initiation of the sweep and returns to the initial condition at its end
(Waveform c, Fig. 12T). This involves a switching action which, as
indicated in Fig. 12T, is usually provided by the same square wave that
turns on the cathode-ray tube.

The timer generates a set of discrete range markers: sharp video pulses
occurring at regular, precisely known intervals. In a self-synchronous
system, the markers must be recycled on each transmitter pulse; this
requires a transient oscillator. In the simple example illustrated, the
square wave b provides the necessary switching voltage. Often the
discrete range markers are supplemented by a continuously variable
range marker which may be generated in any of several ways. As indi¬
cated in Fig. 12T, the markers are usually mixed with the radar video
signals and the combination applied to the cathode-ray tube. In some
cases, however, the signals and the markers are applied separately to
different electrodes of the cathode-ray tube.

The equipment illustrated does not provide for the use of a delayed
sweep. If one is to be used, separate square-wave generators are neces¬
sary to switch the range-marker circuit and to perform the other func¬
tions. The former square-wave generator must be triggered directly as

1 A trigger generator for the modulator is sometimes housed with the indicator
equipment for convenience, but the actual synchronization is accomplished by trans¬
mitting the modulator pulse to the timer proper. This case is functionally identical
with that in which the trigger source is physically part of the modulator.

* Certain modulators, such as the rotary gap, cannot be triggered at all. Other
tvpes can be triggered but have so variable a response time that the modulator pulse
itself must be used for synchronization in order to provide the necessary precision.

Sec. 12-2]

A TYPICAL RECEIVING SYSTEM

439

before. The latter must be provided with a delayed trigger which may
come from a continuously variable timing circuit or may be one pulse of a
discrete set, often the range-marker pulses themselves. The continuous
type of delay is frequently associated with a continuous precision range
marker (Sec. 13T2).

Many deviations from Fig. 12T are possible if the timer provides the
synchronizing pulse. In particular, the discrete range markers can then
be derived from a high-precision c-w oscillator, one of the marker pulses
being selected as the modulator trigger by a scaling-down process. A
continuous marker can also be provided from this oscillator by means of a
continuous phase-shifting device. Other advantages of the timer-con¬
trolled synchronization entail the use of a “pre-trigger” by means of
which the actions of certain circuits can.be initiated somewhat in advance
of the firing of the modulator. Many other functions, some of which
will appear in later sections, are performed by the timer in complex
situations.

The functions of those indicator circuits not included in the timer
vary widely with the different display types. For illustrative purposes,
Fig. 12-1 has been arranged to illustrate a simple A-scope or, alternatively,
a simple B-scope. The former requires no equipment beyond that
already described. The connections to the cathode-ray tube are shown
as position .4 of the switch. The range-sweep voltage is applied to one
pair of deflecting plates and the signal and range-mark voltages to the
other. The square wave controlling the cathode-rav-tube intensity is
applied to the cathode in proper polarity to brighten the tube during the
range sweep.

In the B-scope display, the range sweep is applied to a deflection plate
just as before. Signal modulation is applied to the control grid, and the
second set of deflecting plates receives a voltage that produces the azi¬
muthal deflection. This may be furnished, in simple cases, by a linear
potentiometer geared to the scan axis. Amplification may sometimes be
necessary before applying the azimuth sweep voltage to the cathode-ray
tube. The circuits shown are equally applicable to a magnetic tube, the
only appreciable changes being in the deflection amplifiers.

The timer of Fig. 121 can be used in the production of many other
types of indication. For example, Fig. 12-2 shows the additional parts
necessary to generate one type of PPI, and Fig. 12-3 those necessary for a
(technically) different PPI or, alternatively, for one form of RHI.

The PPI of Fig. 12-2 is of the so-called “rotating coil” type. A single
deflection coil driven by the range-sweep amplifier produces a radial
range sweep. This is made to take the direction on the tube face that
corresponds to the instantaneous antenna orientation by some form of
electromechanical repeater. Except for this modification in the deflec-

440

THE RECEIVING SYSTEM—RADAR RECEIVERS [Sec. 12-2

tion system, the display circuits can be identical with those of the B-scope
of Fig. 121.

Figure 12-3 shows the parts necessary to convert Fig. 12-1 to an
“electronic” PPI without moving parts, or by a slight variation into an
RHI. The range sweep of a PPI can be considered as made up of two
orthogonal sweeps with speeds proportional to sin 6 and cos 9 (see sketch

Fio. 12*3.—Electronic PPI and RHI.

in Fig. 12-3). In this particular form of PPI, these sweep “components”
are formed by passing a sawtooth waveform through a sine-cosine
“resolver” on the scanner. The resolver is a variocoupler or a sine-
cosine potentiometer which, when excited by a given waveform, produces
two “components” of the same waveform whose amplitudes are propor¬
tional respectively to the sine and the cosine of the orientation angle of
the resolver. Proper amplifiers are provided for driving a pair of orthog¬
onal coils (as indicated in Fig. 12-3) or, alternatively, the deflecting
plates of an electrostatic tube.

Sec. 12-3]

SPECIAL PROBLEMS IN RADAR RECEIVERS

441

If elevation angle is substituted for azimuth, the device becomes an
RHI. Usually, in this case, the gain of the vertical amplifier is made
greater than that of the horizontal, so that the display is “stretched” in
the vertical direction. Since direct-coupled push-pull sweep amplifiers
are usually used, they can be biased in such a way as to produce the
“off-centering ” shown.

THE RECEIVER

By W. H. Jordan

12*3. Special Problems in Radar Receivers. —Radar receivers,
though similar in principle to all radio receivers, differ from them in some
respects. This fact is chiefly due to a difference in emphasis on some of
the functions. For example, it would be foolish to design a broadcast
receiver with the ultimate in sensitivity when the weakest signal that can
be detected is determined largely by man-made and natural static. In
the radar portion of the spectrum, on the other hand, external sources of
interference are normally negligible, and consequently the sensitivity
that can be achieved in a radar receiver is normally determined by the
noise produced in the receiver itself. Methods of reducing this noise are
of prime importance in radar receiver design. Not only must noise be
kept down, but everything possible must be done to minimize attenua¬
tion of the signal before it is amplified. How this has influenced the
design of r-f components has already been seen. The effect on the design
of i-f amplifiers will be developed in this section.

The lack of low-noise r-f amplifiers or converters in the microwave
region has meant that most microwave receivers convert the r-f signal
to an i-f signal directly in a crystal mixer and then amplify the i-f signal.
This lack of previous amplification complicates the design of the i-f
amplifier, as is shown by the following expression, given in Chap. 2, for
the over-all receiver noise figure.

A r ov.r-»il = — (A r i-t + T — 1), (1)

where

g = gain of the converter,

T — noise temperature of the converter,

Ni.t = noise figure of the i-f amplifier.

A good crystal in a well-designed mixer will have a noise temperature
T that is only slightly more than 1. This means that the over-all noise
figure is reduced in direct proportion to the reduction in i-f noise figure.
Hence it is important to design the i-f amplifier to have a noise figure that
approaches as nearly as possible the theoretically perfect value of 1.

442

THE RECEIVING SYSTEM—RADAR RECEIVERS [Sec. 12-4

Another very important factor in radar receiver design is that of
securing a good transient response. Reception of pulses about 1 ^sec in
length imposes severe requirements on the pass band of the amplifier.
At the same time, the amplifier must be capable of amplifying pulses
several hundred microseconds in length and yet be fully sensitive to a
weak signal immediately following. It must recover immediately from a
signal thousands of times stronger than the minimum discernible signal.

Frequently special requirements are placed on the receiver. For
example, it may be required that it respond to weak pulses even in the
presence of a c-w signal of considerable strength. The problem of
detecting a weak target echo in the presence of strong sea return is some¬
what similar. Special circuits which go under the general title of “anti¬
clutter circuits” are usually required in such cases.

The unique requirements outlined in the foregoing three paragraphs
have resulted in a receiver that is considerably different from anything
previously existing. The design of i-f and video amplifiers to meet these
requirements will be discussed in the following sections.

12-4. I-f Amplifier Design. —In an ideal i-f amplifier, all the noise
would originate in the generator connected to its input terminals—that is,

the crystal that serves as converter in
the usual radar receiver. In any prac¬
tical amplifier there are additional
sources of noise. Thermal noise from
resistances in the input circuit and shot
noise due to the uneven flow of elec¬
trons to the plate of the first tube are
the chief sources of excess noise, al¬
though later stages may contribute
slightly. For this reason, care must
be taken in the design and tuning of the network coupling the crystal to
the first grid as well as in the choice of the operating conditions and type of

Fiq. 12-4.—Pentode input circuit.

the first tube.

Figure 12-4 shows a typical input circuit, with the primary tuned to
resonate with the crystal and mixer capacity at the intermediate fre¬
quency, and with the secondary tuned to resonate with the input capacity
of the tube and socket. The coils are usually fixed-tuned or “slug-
tuned” 1 in order to avoid any extra capacity. The only loading on the
circuit is due to the crystal and the input resistance of the tube; thus,
there are no additional resistances to contribute thermal noise. Thermal

1 The inductance of a “slug-tuned” coil is lowered by the effect of eddy currents
induced in a metallic rod (slug) inserted in one end of the coil. The degree of penetra¬
tion, and therefore the inductance, can be varied by turning the slug in a threaded
support.

Sec, 12-4]

I-F AMPLIFIER DESIGN

443

noise due to the resistance in the coils themselves can be kept negligibly
small by using coils of moderate Q. The coupling between primary and
secondary is preferably magnetic, since capacitive coupling gives a some¬
what poorer noise figure. The amount of coupling is usually fixed at a
value that gives the best noise figure. This is necessarily greater than
critical coupling, and in the case of a 6AC7 seems to be about transitional
—that is, just before a double hump appears in the pass band. The
bandwidth with this amount of coupling depends upon the crystal resist¬
ance and the mixer and tube capacities. Since the crystal resistance is
small (around three or four hundred ohms), the bandwidth is usually
adequate, being around 10 Mc/sec between half-power points. Con¬
siderably greater bandwidths can be obtained by paying attention to the
mixer capacity.

A number of tube types have been tried in the first stage; however,
most radar receivers today use the 6AC7, 6AK5, or 717. The 6AK5 and
717 are very similar in electrical performance and give a lower noise
figure than the 6AC7; however, the latter is still widely used.

Table 121.—Average Noise Figure

Circuit

Tube type

Intermedi¬

ate

frequency,

Mc/sec

Over-all
receiver
bandwidth, :
Me / sec

Average

noise,

db.

1st

stage .

2nd

stage

Grpunded-cathode pentode to

6AC7

1.5

3.9

grounded-cathode pentode

6AK5

3.3

6AK5

6.5

Grounded-cathode triode to

6AK5

1.5

1 5

grounded-grid triode

6AK5

2.2

6AK5

6J6

3.5

6J4

180

5.5

The operating voltage and current for the first tube are frequently
influenced by design considerations other than noise figure. In general,
the plate and screen voltage should be low (75 to 120 volts are common)
and the cathode current should be as high as is permitted by the tube
ratings.

The noise figure that can be obtained by use of the circuit shown in
Fig. 12-4 depends upon the intermediate frequency and the over-all
receiver bandwidth. Since it varies considerably with individual tubes
of the same type and manufacture it is desirable to quote average figures.
Some representative values are given in Table 12T.

It has long been realized that a large portion of the shot noise in a
pentode is due to the interception of electrons by the screen grid. Hence.

444

THE RECEIVING SYSTEM—RADAR RECEIVERS [Sec. 12-4

a triode is less noisy than a pentode. The difficulty in using a triode lies
in finding a circuit that is stable, uncritical in adjustment, yet with
enough gain to swamp out noise originating in the following stage. A
circuit that has recently been developed is shown in Fig. 12-5. The input
transformer T is similar to the one used for pentodes. In order to realize
the ultimate noise-figure capabilities of the circuit, the Q of the coils
must be kept high.

The circuit shown in Fig. 12-5 consists of a grounded-cathode tri¬
ode working into a grounded-grid triode. The input impedance of a
grounded-grid amplifier stage is very low, being approximately l/g m , or
200 ohms for a 6AK5. Since this impedance loads the first stage so
heavily that its voltage gain is about 1, there is no tendency for it to

The loading is so heavy that the
interstage bandwidth is very great.
Since the value of L 2 is thus non-
critical, the circuit is, in fact, fixed-
tuned. Inductance L 3 is an i-f
choke of almost any characteris¬
tics. Thus the circuit is stable
and uncritical; it only remains to
be shown that the noise contri¬
bution of the second triode is
small. This is not obvious, and a
rigorous proof is beyond the scope
of this book (see Yol. 18 of this
series). In order to minimize the
second stage noise, the impedance
seen when looking back from the cathode of the second triode must be
large compared to the equivalent noise resistance at this cathode. To
make this impedance as high as possible, an inductance L x is connected
between plate and grid of the first triode. Inductance L x resonates with
the plate-grid capacity at the intermediate frequency. This inductance
is not needed for stability but does improve the noise figure about 0.25 db.

Noise figures obtainable with the double-triode circuit depend on
several factors; representative values are shown in Table 12T. Improve¬
ments of 2 db or more over the pentode circuit are usual.

Before describing the i-f amplifier, a brief discussion of some of the
factors involved in choosing the intermediate frequency will be given.
The over-all receiver bandwidth should be from 1 to 10 Mc/sec to pass
the pulses ordinarily encountered in microwave radar sets. 1 An inter-

1 In this chapter i-f amplifier bandwidth will be taken between the half-power
points; video amplifier bandwidths will be measured between the frequencies at
which the video response is 3 db down. The over-all receiver bandwidth (i.e., the

oscillate, even without neutralization.
B+

Sec. 12-4]

I-F AMPLIFIER DESIGN

445

mediate frequency considerably greater than this is required in order that
i-f sine waves can be filtered out of the video amplifier. Local-oscillator
noise can be minimized by the use of a high intermediate frequency;
however, the balanced mixer (cf. Vol. 16 of this series) provides a better
solution to this problem. Many of the present AFC systems require the
use of a high intermediate frequency to prevent locking on the wrong
sideband. Finally, components such as condensers and coils become
smaller as the frequency is raised, a distinct advantage in lightweight
airborne radar sets. On the other hand, there are at least two very cogent
reasons for favoring a low intermediate frequency: (1) the noise figure
of the i-f amplifier is smaller at lower frequencies, and (2) manufacture
and maintenance is considerably simplified because variations in tube and
wiring capacitances, as well as in tuning inductances, affect the over-all
receiver response much less’ Thus the choice of an intermediate fre¬
quency is a compromise. Frequencies
of 30 Mc/sec and 60 Mc/sec have been
chosen for most of the present-day
radar sets. The i-f amplifier band¬
width is not an important factor in
the choice of the intermediate fre¬
quency. It is just as easy to achieve
a bandwidth of, for example, 5 Mc/sec

at a center frequency of 5 Mc/sec as it
is at 60 Mc/sec. Fl °' ^ 6 .-Sin g le-tuncd i-f amplifier.

An i-f amplifier consists of a number of cascaded stages. Figure 12-6
is a circuit diagram of a type of stage in common use.

This is known as a single-tuned stage, since there is one tuning
inductance per stage. It has the advantage of being simple, easy to
manufacture and align, and noncritical in adjustment. It is particularly
useful in i-f amplifiers of over-all bandwidth less than 3 Mc/sec. It
becomes expensive at wider bandwidths, although an improvement in
tube performance would raise this figure proportionately.

The inductance L is tuned to resonate at the intermediate frequency
with the combined output and input capacity plus stray capacity to
ground due to sockets and wiring. It is placed in the grid circuit to
provide a low-resistance path to ground. Thus, when the grid draws
current during a strong signal, it does not accumulate a bias; hence the
gain is not reduced and the amplifier remains sensitive to weak signals.

The gain G of the single-tuned stage shown in Fig. 12-6 is given by the
expression

G = g m R L , (2)

combined response of the video and i-f amplifier) will be taken as the equivalent i-f
amplifier bandwidth unless otherwise stated.

446

THE RECEIVING SYSTEM—RADAR RECEIVERS [Sec. 12 4

and the bandwidth by the equation

ffi =

1 1
2x R l C'

(3)

where C is the total capacity resonated by L.
product is

Hence the gain-bandwidth

(4)

From Eq. (4) we can see the necessity of using tubes with as high a
ratio of transconductance to input-plus-output capacitance as possible.
The 6AK5 is slightly better than the 6AC7 in this respect, average tubes
giving gain-bandwidth products of approximately 55 Mc/sec and 50
Mc/sec, respectively, when allowance is made for socket and wiring
capacity. One can also see from Eq. (4) the necessity of keeping extra¬
neous capacities to a minimum. It is for this reason that the inductance
L is either fixed-tuned or slug-tuned, instead of being used with a tuning
condenser. By the same token, the use of point-to-point wiring and the
mounting of components on the tube sockets are clearly indicated.

Amplifiers with a gain of 120 db and an over-all i-f bandwidth of about
2 Mc/sec will require a stage bandwidth of over 6 Mc/sec, which permits
a gain of approximately 7, or 17 db. Thus seven stages will be required.
Assuming a g m of 7000, a reasonable figure for a 6AC7, the load resistance
Rl would be 1000 ohms [Eq. (2)].

Many more stages would be required to increase this bandwidth
greatly, since the gain per stage must be lowered. The over-all band¬
width of an amplifier consisting of cascaded single-tuned stages is given
approximately by the formula

„ „ , . .,,, single-stage bandwidth

Over-all bandwidth = — --—==-— (4)

1.2 Vn

When n, the number of cascaded stages, is larger than 3, this formula is
quite accurate.

Thus the number of single-tuned stages needed in an amplifier of
given gain, even for moderately wide bandwidths, becomes prohibitively
large. Lacking better tubes, the only alternative lies in the use of more
effective circuits. Two things are needed: (1) a coupling circuit that
will give a greater gain-bandwidth product for a given tube, and (2) a
response-vs.-frequency curve that, when cascaded, does not narrow as
rapidly as that given in Eq. (4). The double-tuned (transformer-
coupled) circuit does very well in these respects. The elements of the
usual double-tuned circuit are shown in Fig. 12-7.

The primary is tuned to resonate with the capacity in the plate cir¬
cuit, the secondary with the capacity in the grid circuit. The coupling

Sec. 12-4]

I-F AMPLIFIER DESIGN

447

is varied to give the desired response characteristic, usually that obtained
just before the curve becomes double-humped. The loading R p and R,
may be divided as shown, or placed on one side only. Two cases will be
considered: (1) both sides are loaded so that the Q of the primary is equal
to the Q of the secondary; (2) the loading is on one side only. With
transitional coupling 1 the shape of the response curve is the same in either
case, but the gain and bandwidth are
not.

In the case of equal Q’s on both
sides, the gain is given by

G = Vif’ (5)

where C p and C, are the circuit ca¬
pacities associated with primary and
secondary respectively. The bandwidth is

1 V2

(B =

2ir R P C P

( 6 )

Hence the gain-bandwidth product is

fix®

Qm __ 1

2* V2

( 7 )

If the loading is entirely on one side, either primary or secondary, the
above equations become

G = g m V2R P

(8)

1 1

® = 6 - 7=->

2* V2R P C P

(9)

X ® = 7?—^ -

2ir Vc P c,

(10)

If one compares the gain-bandwidth products given above with those
previously quoted for single-tuned circuits, it will be seen that there is an
improvement by a factor of 3.8 db in the equal-Q case and by a factor of
6.8 db in the case of loading on one side only. 2 There is the further

t As the coupling between two circuits of unequal Q is increased from zero, the
response at resonance rises to a maximum at the “critical coupling” point and then
decreases (with a flatter and flatter top to the response curve) until the point of
“transitional” coupling is reached, after which the curve becomes “double-humped.”
If the two circuits have equal Q’s, transitional coupling and critical coupling are
the same.

2 Values of C p and C 9 of 7 and 14 nn f, respectively, were used for this calculation.

448 THE RECEIVING SYSTEM—RADAR RECEIVERS [Sec. 124

advantage that cascaded double-tuned circuits do not narrow as rapidly
as cascaded single-tuned circuits because of the rectangular form of the
response curve (Fig. 12-8). For example, nine cascaded single-tuned
stages, each of 6-Mc/sec bandwidth, would have an over-all bandwidth
of 1.7 Mc/sec. However, nine cascaded double-tuned circuits, each 6
Mc/sec wide, would combine to give a 3.2-Mc/sec over-all bandwidth.
The over-all bandwidth of n cascaded double-tuned circuits is given by

Over-all bandwidth = giSg l S^age bandwidth

1.1 y/n

The usefulness of double-tuned circuits in wideband amplifiers has
been demonstrated by their incorporation in a radar receiver having 120

ta) Single tuned (A) Double tuned (c) Stagger tuned

Fig. 12-8.—-Amplifier response curves.

db of i-f amplifier gain and an over-all bandwidth of 12 Mc/sec. This
was accomplished with only nine 6AK5 tubes in the i-f amplifier (Sec.
12-11). On the other hand, there are disadvantages in using double-
tuned circuits. They are difficult to align, special equipment being
required. Though this can be circumvented to some extent in wideband
amplifiers by the use of fixed tuning, the sensitivity to variations in tube
capacity and coil inductance is much greater than that of single-tuned
circuits. This is particularly true when the loading is on one side only,
so that this arrangement is ordinarily used only in very wideband ampli¬
fiers (15 Mc/sec or over).

Another means of achieving large bandwidth is by using stagger-
tuned circuits. 1 Consider two cascaded single-tuned circuits of the type
previously described, choosing the load resistors so that each has a band¬
width of 4 Mc/sec as shown in Fig. 12-8. The combined response curve
of the two stages will be the product of the responses of the individual
stages and is shown by the dashed line.

1 H. Wallman, RL Report No. 524, Feb. 23, 1944.

Sec. 12-5]

SECOND DETECTOR

449

This combined response curve has the same shape as that for a transi¬
tionally coupled double-tuned circuit, so that the advantage of cascading
is preserved. In actual practice, a receiver that has a gain of 100 db with,
for example, six stages, will be approximately twice as wide if staggered
pairs are used as it would be if single-tuned circuits were used (Fig. 12-8).

The principle of stagger tuning can be carried further. Staggered
triples (three different frequencies) are in fairly common use, and stag¬
gered w-uples are practicable for wideband amplifiers. The advantage
of stagger-tuned amplifiers lies in the fact that simple single-tuned cir¬
cuits are used throughout, a fact that makes for ease of manufacture and
servicing.

There are other schemes for obtaining large bandwidths. Feedback
pairs 1 and feedback chains 2 3 * have both been used fairly extensively.
More recently a scheme of stagger damping has been proposed. !

Before leaving the problem of i-f amplifier design, some mention of the
gain required will be necessary. To detect signals barely visible above
the noise it is necessary that the noise originating in the input circuit and
the first stage be amplified to a point where it is easily visible on the indi¬
cator. How this gain will be split between the i-f and video amplifiers
depends upon such considerations as second-detector efficiency and the
complication involved in building high-gain video amplifiers. In most
receivers the i-f gain is enough to amplify noise to 1 or 2 volts, thus bring¬
ing it into the linear region where diode detectors have maximum effi¬
ciency. This requires a gain of around 10 6 times at the intermediate
frequency. Building an i-f amplifier with this gain while avoiding trouble
with regenerative feedback has been one of the most difficult problems in
radar receiver design. Ground current loops must be confined by careful
bypassing and grounding; power leads must be properly filtered; coils
must be wound and spaced intelligently; the shielding must be adequate.
Careful attention must be paid to all of these items if the over-all response
characteristic is to bear any resemblance to what is expected.

12-5. Second Detector. —The purpose of the second detector is to
produce a rectified voltage that is proportional to the amplitude of the
i-f waves. In most receivers it is important that this rectified voltage be
proportional to the first power of the i-f amplitude (linear detector).
However, in radar receivers higher powers are permissible so long as
reasonable efficiency is maintained. One of the simplest and most com-

1 Bartelink el. al., “Flat Response Single Tuned I-f Amplifier,” GE Report, May 8,
1943.

* A. J. Ferguson, “The Theory of I-f Amplifier with Negative Feedback,” Cana¬
dian National Research Council Radio Branch Report PRA-59.

3 H. Wallman, “Stagger-damped Double-tuned Circuits,” RL Report No. 536,

March 23, 1944.

450

THE RECEIVING SYSTEM—RADAR RECEIVERS [Sec. 12-6

monly used second detectors is the diode detector shown in Fig. 12-9.
The diode is usually a tube such as the 6H6 or the 6AL5, although many
other tubes have been used and recently crystals have been developed
for the purpose. The i-f bypass condenser C usually has around 10
nni of capacity; it must be considerably larger than the plate-to-cathode
capacity of the diode to get good detector efficiency, but it must not be so

large as to spoil the high-frequency
response of the video amplifier. The¬
oretically, the high-frequency response
would be maintained, however large
C, by making R proportionally smaller.
If R is too small, however, the detec¬
tion efficiency is lowered and the max¬
imum voltage that the detector can
produce becomes too low. Values of R from a few hundred to a few
thousand ohms are usual. Inductance L 2 is chosen to offer a high
impedance at the intermediate frequency and is sometimes made resonant
at this frequency.

12-6. Video Amplifiers. —One or more stages of video amplification
follow the detector. The form of the video amplifier is determined largely
by the number and location of the indicator tubes. In an airborne radar
set there may be only a single indicator located near the receiver, in which
case the video amplifier is very simple. In large ground and ship sets
there will be many indicators located far from the receiver, and the video
amplifiers must be more complex. In the latter case, the video amplifier
following the detector drives a terminated line at a level of a few volts,
and individual indicators are driven by video amplifiers bridged across
this line.

The requirements placed on a video amplifier can be stated quite
generally.

1. A signal of a few volts from the detector must be amplified and
transmitted to the indicator, the signal level at the indicator being
usually about 20 volts, although some types of indicator require a
much higher voltage.

2. The amplifier must have good transient response, as defined by
the following: it must pass long pulses with little “droop” on the
top of the pulse; this requires good low-frequency response. The
rise time 1 must be definitely shorter than the pulse length, and the
overshoot on a pulse should be held to 10 per cent or less; these
factors are determined by the high-frequency response. The

1 Rise time is conveniently defined as the time required for the output voltage of
the amplifier to rise from 10 per cent to 90 per cent of its final value when a square
pulse is applied to the input.

To video

Sec. 12-6] VIDEO AMPLIFIERS 451

amplifier must recover from large signals quickly, requiring that
no control-grid current be drawn on strong signals.

3. Some form of limiting must be provided. The noise voltage at
the output of the detector will be approximately 2 or 3 volts peak.
In order that the noise be clearly visible on the screen, it must be
amplified sufficiently to drive the indicator tube over something
like half its allowable control-grid voltage swing. Since signal
voltages from the detector may be 20 volts or more, the output
voltage must be limited so that the indicator will not be driven
outside its allowable range of voltage.

The simplest and most commonly used type of video amplifier is the
resistance-capacitance-coupled am¬
plifier shown in Fig. 12T0.

Although the gain for small sig¬
nals can be simply expressed in terms
of the tube and circuit constants, it
is usually determined by reference to
the characteristic curves of the tube.

For many reasons, the high-frequency
performance is most conveniently
expressed by giving the frequency
at which the gain is down 3 db (volt¬
age down to 0.707). This will be
referred to as the “cutoff frequency.”

For the amplifier shown this occurs when

f = 2^RC’ (11)

where R = parallel resistance of R v and R g , and C is the total capacity to
ground which includes output and input capacities plus stray capacities.
Again the need for keeping the stray capacity to a minimum is apparent.
This is sometimes difficult when large coupling condensers or lofig leads
are involved.

There are other coupling networks that will increase the cutoff fre¬
quency and yet preserve the same gain. Perhaps the simplest of these
is the “shunt peaking” circuit, which uses an inductance in series wfith
the load resistor, R p . Let the parameter M be defined by the equation

L = MR 2 C. (12)

Then M can be used as a measure of the performance of the circuit.
Since a value of M = 0.25 corresponds to critical damping, it produces
no overshoot and yet increases the cutoff frequency by a factor of 1.41.
A value of M = 0.41 is the highest that can be used without puttinga hump

452

THE RECEIVING SYSTEM—RADAR RECEIVERS [Sec. 12-6

in the response curve. This value of M increases the cutoff frequency
to a value of 1.73 times that of the simple RC circuit, but produces a 2.5
per cent overshoot on the pulse (the same amount as that produced by a
transitionally coupled i-f stage).

Still greater bandwidths can be obtained by the use of series peaking 1
or a combination of series and shunt peaking. These circuits are more
difficult to use, however, and the reader is referred to Vol. 18 of the Radia¬
tion Laboratory Series for details.

In order to preserve good response to long pulses, it is necessary that
the time constant of the coupling circuit, C c (Rl + R s ), be kept large com¬
pared to the duration of the longest blocks of signals involved. In this
event, the fractional amount of droop on the top of the long pulse is just
the ratio of the pulse length to the coupling time constant. Thus if the
time constant were 50,000 nsec while the pulse length was 1000 psec, the
pulse would droop 2 per cent. This is a reasonably small amount, but
if there were five such circuits in cascade between the detector and the
CRT, then the total amount of droop would be 10 per cent. Although
it is fairly easy to maintain such long time constants provided R L + R g
is large, occasionally it happens that R L + R a is fairly small. This
means that C c must be large, which may result in a large capacity to
ground and affect the high-frequency response. For example, a 1-pf
condenser may have several hundred micromicrofarads of capacity to its
shell. Mounting the condenser on insulating posts is frequently necessary
in such cases.

Another way of reducing the amount of droop on the pulse is by using
low-frequency compensation circuits. In Fig. 12T0, if Rb and C B are
chosen properly, the beginning of the pulse will be flat and the time for the
pulse to fall to 90 per cent will be greatly increased. The value of Cb
must be chosen to satisfy the relation

C b R v = C c R„. (13)

The value of Rb is not specified,.but the amount of droop becomes less
as Rb is increased. However, even for R a — R,, the time for the pulse to
fall to 90 per cent is increased by a factor of 5 over the uncompensated
network.

The limiting of video output signal level is usually accomplished by
applying negative video pulses to the grid of a tube. When the pulses
are large enough to drive the tube to cutoff, the output pulse remains
constant in amplitude, no matter how much larger the input pulses may
be. If the circuit shown in Fig. 12T0 were connected to the detector of
Fig. 12-9, it would serve very well as a limiter-amplifier. With a sharp-
cutoff tube whose screen is operated at low voltage (75 to 100 volts),

1 In series peaking a compensating network is placed in series with the two stages.

Sec. 127]

AUTOMATIC FREQUENCY CONTROL

453

signals of 4 or 5 volts peak reach the limit level. It is wise to have a
limiter very early in the video amplifier, for then the following stages are
protected from excessively large signals.

Self-bias is frequently used in a video amplifier, but, since a condenser
of sufficient capacity to prevent degeneration at the lower frequencies
would be prohibitively large, such a condenser is usually omitted entirely
in order to assure uniform frequency response.

When the indicator is some distance from the receiver, the two are
usually connected by a line terminated in its characteristic impedance.
Unterminated lines have been used, but the high-frequency response is
greatly impaired. Although lines of 1000-ohm characteristic impedance
have been made and are fairly satisfactory for lengths of 20 ft or less,
longer lines are usually standard 75- or 100-ohm coaxial cable. To drive
such a line from the plate of an amplifier requires a very large coupling
condenser; hence the cathode-follower circuit shown as the second stage
in Fig. 1210 is ordinarily used (see Sec. 13-6). Its chief advantage is
that it can be direct-coupled. Although the gain is considerably less
than 1, this is not appreciably less than would be obtained with a plate-
coupled amplifier working into such a low impedance.

Following the line and bridged across it are the video amplifiers
associated with each indicator. Since these amplifiers can be located
very near to the control electrode of the CRT, stray capacities can be
kept very small. These amplifiers can thus be either grounded-grid or
grounded-cathode, depending on the polarity of signal desired.

12-7. Automatic Frequency Control. 1 —The over-all bandwidth of a
radar receiver may be determined by the bandwidth of either the i-f or
the video circuits. However, for the purposes of this chapter we need
only be concerned with the i-f amplifier, since we are interested here in
questions of stability rather than in the quality of signals. As dic¬
tated by the principles outlined in Sec. 2-22, bandwidths of 1 to 4 Mc/sec
are common. The narrowest r-f component, a high-Q TR switch, is so
much wider than this that, once adjusted, no drifts large enough to cause
serious detuning are likely to occur over a period of a day or so. The
problem of keeping a radar in tune, then, consists essentially in maintain¬
ing the difference between the magnetron frequency and the local-
oscillator frequency constant and equal to the intermediate frequency,
with an accuracy of 1 Mc/sec or better. There are two reasons for mak¬
ing the tuning automatic. The first is that as the antenna scans, varia¬
tions in standing-wave ratio arising from asymmetrical rotary joints or
reflections from near-by objects can pull the magnetron several mega¬
cycles per second. Manual tuning is so slow relative to scanning that it
brings in only part of the picture at a time. Second, whether or not

1 By A. E. Whitford.

454

THE RECEIVING SYSTEM—RADAR RECEIVERS [Sec. 127

pulling exists, the magnetron and local oscillator will not hold constant
frequency to one part in several thousand for several hours, nor will they
vary together in some predictable manner. Variations in voltage, tem¬
perature, and pressure all produce frequency changes. Frequent tune-up
by the operator, using echoes, is not dependable since serious deteriora¬
tion in the sensitivity of a radar, such as that caused by drifting out of
tune, is not immediately obvious on the scope. Also, in a ship on the
open ocean or in an airplane over the ocean, there may often be no

targets to provide echoes.

For these reasons, an automatic-
frequency-control circuit, AFC, has
come to be a standard part of all radar
sets. It is an electronic servo-mech¬
anism that tunes the local oscillator in
such a way that the proper difference
frequency between it and the mag¬
netron is maintained. The speed of
tuning can usually be great enough to follow any pulling of the magnetron
that may occur during the scanning cycle.

In the case of beacon reception, automatic frequency control main¬
tains the local oscillator at a predetermined frequency that is higher or
lower than the frequency of the distant beacon transmitter by just the
intermediate frequency.

Radar AFC .—All forms of radar AFC work on the same basic prin¬
ciple. Part of the local-oscillator power is mixed, in a crystal, with a
small fraction of the magnetron power drawn out during transmission
of the pulse. The difference frequency is applied to a frequency-dis¬
criminator circuit whose crossover is set at the intermediate frequency.
The variation of the height of discriminator output pulses as a function
of local-oscillator frequency is shown in Fig. 12T1.

These pulses are integrated or otherwise converted to a voltage, which
is applied to a control electrode of the local oscillator in the proper sense
to push the frequency toward the crossover of the discriminator curve.
This makes a degenerative feedback loop, and the frequency of the local
oscillator is held very near the crossover point on the curve.

As shown in Fig. 11-22 (Sec. 11-7), the voltage on the reflector of a
reflex klystron of the type used as a local oscillator tunes the tube over a
range of about 30 to 70 Mc/sec. Some local oscillators are also thermally
tuned by means of a control electrode which is the grid of an auxiliary
triode. This provides slow tuning over a much wider frequency range
(see Vol. 7 of this series).

A block diagram of a typical AFC system is shown in Fig. 12-12.
The dotted portions are the additions necessary to include beacon AFC

Fig. 12*11.—Height of discriminator
output pulses, where/o is the transmitter
frequency and is the intermediate
frequency.

Sec. 12-7]

AUTOMATIC FREQUENCY CONTROL

455

in the system; these will be discussed in the next section. In the simplest
type of radar AFC, the integrated discriminator pulse output, suitably
amplified, would go directly to the reflector of the local oscillator. This
“hold in” type of AFC requires manual tuning each time the radar is
turned on. The sawtooth generator shown in the block diagram con¬
verts the circuit to the more desirable “search and lock” type. The
sawtooth “sweeps” the local-oscillator frequency until the change in
polarity of the discriminator output when “crossover” is reached results

in signals of proper polarity to operate a circuit which stops the sawtooth.
This circuit will find the correct frequency if crossover is anywhere
within the electronic tuning range of the local oscillator. Half a second
is a typical period of one sawtooth search cycle.

The r-f part of the block diagram shows a double mixer that has
separate crystals for the radar and AFC functions, both receiving power
from the radar local oscillator. This permits the AFC crystal to be
operated at a predetermined power level. The alternative—taking the
AFC information from the output signal of the radar crystal arising
from transmitter power that leaks through the TR switch—has been
used but suffers from serious disadvantages. The leakage power may
be 10 to 20 times that desired for most favorable operation of the crystal,
and is variable from one TR tube to another. An even more serious
difficulty is caused by the “spike” energy, which, because it occurs as an
extremely short pulse, contains a very wide range of frequency com¬
ponents. Spurious frequencies present in the spike mask the desired
information. A successful corrective has been to suppress the i-f amplifier

456

THE RECEIVING SYSTEM— RADAR RECEIVERS [Sec. 12-7

for the beginning of the pulse and to accept a signal only from the latter
part. This requires accurate timing and becomes very difficult for
short pulses.

A satisfactory operating level for the AFC crystal is 0.5 mw c-w
power from the local oscillator and 1 to 2 mw pulse power from the mag¬
netron. Reduction of the magnetron power level by 65 to 90 db below
the transmitted power is obtained by a combination of weak coupling out
of the main r-f line and an attenuator, preferably dissipative. It is
important that the r-f system be tight in order to prevent leakage power,
possibly many times that desired, from reaching the crystal by stray
paths. This becomes easier if the operating level of the AFC crystal is
made as high as is permissible. A high operating level also requires less
i-f gain ahead of the discriminator and thereby reduces the effect of gain
variations.

Too high an operating level is, however, undesirable because as the
crystal is driven up to 10 mw or above, it saturates. The harmonics of
the difference frequency then become stronger relative to the funda¬
mental. For example, if the discriminator crossover is set at 30 Mc/sec,
corresponding to an i-f amplifier centered at that frequency, a second
harmonic at 30 Mc/sec large enough to actuate the control circuit and
cause locking may appear when the local oscillator is only 15 Mc/sec
away from the magnetron frequency, under conditions of AFC crystal
saturation.

The gain of the AFC feedback loop should be high enough to insure
tight locking but not so high that the second harmonic can also cause
locking. At the recommended level of 1 to 2 mw of magnetron power
the harmonics are at least 20 db below the fundamental. A gain control
is undesirable; therefore, care in controlling the r-f power levels and in
amplifier design is required for a foolproof AFC. The most frequent
sources of trouble are usually on the r-f side rather than in the electronic
circuits, and arise from high power leakage into the crystal, faulty
coupling to the main line, or a wrong amount of attenuation.

Beacon AFC .—To hold the beacon local oscillator at a given absolute
frequency, some r-f reference standard must be provided, since the mag¬
netron involved is in the beacon, distant from the radar. At microwave
frequencies the reference standard is a resonant cavity. With proper
attention to details such as temperature compensation and moisture
sealing, production-line cavities can be depended upon to maintain a
specified frequency to 1 or 2 parts in 10,000.

The dotted portion of Fig. 1212 shows the beacon local oscillator
attached both to the radar crystal and, through the reference cavity, to a
beacon crystal. The output of the beacon crystal as a function of fre¬
quency is shown in Fig. 1213. It is, of course, just the simple resonance

Sec. 12 SI PROTECTION AGAINST EXTRANEOUS RADIATIONS

457

curve of the cavity. Under actual conditions of loading, the width A f
between half-power points is commonly about tttbt of the resonant fre¬
quency itself.

Any control circuit that will lock the beacon local oscillator at the
top of the resonance curve must in some manner take a derivative of the
curve. The derivative, shown dotted in Fig. 1213, has the same shape
as the usual discriminator curve. In the scheme shown in the block
diagram, a 1000-cycle sine wave from an a-f oscillator is added to the
slowly varying voltage from the sawtooth search oscillator. This sweeps
the local-oscillator frequency over a range that may be a tenth of the
half-power bandwidth of the cavity. The crystal output then has an
amplitude modulation of magnitude proportional to the slope of the
cavity resonance curve at the frequency in question. The phase of this
amplitude modulation depends on whether the slope is positive or nega¬
tive. The output signal from the crystal goes to one grid of a coincidence
tube, another grid of which receives the same sine wave used for modulat¬
ing the local-oscillator frequency.

Only when the two coincide in phase
will the coincidence tube conduct.

As the frequency of the local oscilla¬
tor drifts across the cavity resonance
curve, the coincidence tube gives no
output signal on the rising side of the
curve, and passes 1000-cycle pulses
increasing in amplitude as the top is
crossed and the slope becomes nega¬
tive. The pulse integrator uses these
at a voltage that produces a local-oscillator frequency very near the top
of the cavity resonance curve.

12-8. Protection against Extraneous Radiations. Antijamming .—
Although the sensitivity of a radar receiver is normally limited by the
noise produced in the receiver, extraneous radiation may be occasionally
picked up on the radar antenna. Such radiation may, for example, be
the result of the operation of other microwave equipment in the vicinity.
It is good design practice to protect against such interference, and, as
will be seen later, the same provisions are sometimes of value in the
absence of interference. These AJ (antijamming) provisions may
merely be precautions taken in the design of the receiver which do not
affect its normal operation, or they may be special AJ circuits that can be
switched in and out of use.

Interference may be any of several types such as CW, amplitude-
modulated CW, frequency-modulated CW, r-f pulses, or noise-modulated
CW. The more nearly the interference is like the echoes being received

Fig. 12-13.—Beacon crystal current.

signals to stop the sawtooth sweep

458

THE RECEIVING SYSTEM—RADAR RECEIVERS [Sec. 12-8

or like the noise produced in the receiver, the more difficult it is to dis¬
criminate against.

One type of interference that must be guarded against is “hash,”
from rotating machinery and steep pulse wavefronts, which may leak
into the i-f amplifier. Strict attention must be paid to shielding, and
all leads into the receiver must be properly filtered and bypassed.

Perhaps the most fundamental AJ provisions are those that will
permit the receiver to operate in the presence of considerable amounts of
c-w power. If the second detector is directly coupled to the video

amplifier, then a very small amount
of c-w signal will develop enough
voltage across the detector to bias the
first video stage out of its operating
range. This can be avoided by de¬
veloping an equal amount of counter¬
bias, or by coupling the detector to
the video amplifier through a block¬
ing condenser. The latter course is
much simpler and usually is the one
adopted. The receiver will now continue to function in the presence of a
c-w signal until the i-f amplifier is overloaded. The i-f overload limit
can be increased by operating the last stage or two with higher plate-
supply voltage. Frequently a power tube, such as the 6AG7, is used in
the last stage to increase the output capabilities of the i-f amplifier,
although the 6AK5 has proven fairly satisfactory in this application. A
rather wide video bandwidth (at least as wide as the total i-f bandwidth)
is necessary when the frequency of the jamming signal is not the same as
that of the radar transmitter. Use of a linear detector will also give the
i-f amplifier a greater dynamic range. In some receivers it is necessary
to apply a “gate,” which sensitizes the receiver during a certain interval
of time. It is desirable that such gating be done in the video amplifier
rather than in the i-f amplifier, to avoid generating a pulse when a c-w
signal is present. Finally, the operation of the gain control early in the
i-f amplifier is of value when strong c-w signals are present. The gain
control should be of a type that does not reduce the output capabilities
of the controlled stages; grid gain control is satisfactory in this respect.

The precautions mentioned thus far constitute good design practice
and can well be included in any radar receiver. To protect against either
frequency- or amplitude-modulated c-w signals, such precautions are still
necessary but not quite sufficient. In addition, there is needed between
the detector and video amplifier a filter that will pass individual pulses
but not the c-w modulation frequencies. Several types of filter have
been tried; the simplest is the fast time constant (FTC) circuit shown in
Fig. 12-14.

RFC 51

Fio. 12-14.—Fast-time-constant circuit.

Sec. 12-8] PROTECTION AGAINST EXTRANEOUS RADIATIONS

459

With the switch in the position shown, the time constant of the
coupling circuit is 10,000 Msec so that moderately long blocks of signal
will be passed. With the switch reversed, the time constant is 1 Msec
so that individual pulses will be passed with some differentiation; long
pulses and modulation frequencies below 20 kc/sec will be greatly atten¬
uated. Even for modulation frequencies as high as 200 kc/sec, the
circuit has considerable effect. It should, therefore, be switched in only
when interference makes it necessary.

To plate of last i-f stage

Fig. 12-15.—Instantaneous automatic gain control.

Differentiation circuits, of which the FTC circuit described above is a
good example, are of real value so long as the i-f amplifier is not over¬
loaded. When overloading occurs, the gain of the receiver must be
reduced. As long as the jamming signal is constant in amplitude, manual
gain control is a very satisfactory means of accomplishing the gain reduc¬
tion. However, if the radar antenna is scanning or the c-w signal is
modulated, manual control is much too slow to be effective. For this
reason, various schemes for reducing the gain automatically and rapidly
have been devised. These are variously called “ instantaneous automatic
gain control (IAGC)," “amplified back-bias,” “back-bias,” etc. The
circuit shown in Fig. 12T5 shows the essential elements of an IAGC
circuit.

Signals appearing at the output terminals of the last i-f stage are
rectified by the detector and applied as a negative voltage to the grid of
the cathode follower, which in turn controls the grid bias of one of the
i-f amplifiers in such a way that the presence of a signal tends to lower
the i-f gain. The time required for this reduction in gain to take place is
determined by the constants of the circuits, as well as by the strength of
the signal. In the particular example shown, this time is a few micro¬
seconds, so that the gain is not appreciably reduced by a single pulse but
is cut down by long blocks of signals or by a c-w signal modulated at a
low frequency.

The detector shown in Fig. 12-15 may be either the normal signal-
detector or a separate detector. The output of the IAGC circuit may
be fed back to the grid of the last stage or to that of the preceding stage.
(Instability results from feeding back across too many stages.) When

460

THE RECEIVING SYSTEM—RADAR RECEIVERS [Sec. 12 8

it is necessary to prevent earlier stages from becoming overloaded, they
can be shunted by another similar loop. The gain of the feedback loop
can be increased either by using a plate detector instead of a diode, or by
converting the cathode follower into a d-c amplifier. With a single
feedback loop over two i-f stages, the loss in signal detectability resulting
from a 60-db c-w jamming signal is only 12 db.

Although considerable thought and effort have gone into the problem
of designing a receiver that can discriminate against more complex types
of interference (pulses and noise), this is a much more difficult problem
which will not be treated here. 1

Anticlutter Circuits. —Land, rough sea, and storm clouds reflect a
considerable amount of r-f energy and can, therefore, interfere with the
detection of objects in the area they occupy. If the desired signal is
weaker than the “clutter” from the land, sea, or cloud, it is difficult to
modify the receiver to discriminate against the clutter; for the frequencies
contained in the clutter echoes are in the same range as those of the
desired signals. If, on the other hand, the signal return is larger than
the clutter, it should be possible to see the signal. However, the signal
can be missed if the clutter is so strong as to saturate the receiver com¬
pletely. This can be avoided by reducing the receiver gain to the point
where the clutter is below saturation. Such a procedure would be satis¬
factory if the clutter were everywhere uniform, which it never is. There¬
fore, if the gain is reduced to the point required by strong clutter, it will
be too low for regions of loss or no clutter, and weak signals will still be
lost. The IAGC circuit previously described is very valuable under such
conditions and has been included in many receivers primarily for this
reason.

In the case of sea return, the clutter is fairly constant at all azimuths.
Also, the amount of sea return is a steadily decreasing function of range.
It is possible to devise a circuit that lowers the receiver gain immediately
following the transmitter pulse and then increases it steadily, arriving at
maximum gain at the time the sea return has disappeared. This is
known as a “sensitivity-time-control (STC) circuit”; it has the disad¬
vantage that controls must be provided to adjust it for varying sea condi¬
tions. Nevertheless, STC has proven of considerable value at sea, and
has also been used on some ground-based radar sets where control of air¬
craft close to the set is desired.

TYPICAL RECEIVERS
By W. H. Jordan

The practical application of the foregoing considerations will be illus¬
trated by describing a few typical receivers chosen to cover a wide variety
of purposes.

1 See Microwave Receivers, Vol. 23, Chap. 10.

Sec. 12-8] PROTECTION AGAINST EXTRANEOUS RADIATIONS 461

Fia. 12*16.—General-purpose receiver, (a) Side view; ( b ) top view; (c) bottom view.

462

THE RECEIVING SYSTEM—RADAR RECEIVERS [Sec. 12-9

12-9. A General-purpose Receiver. —This receiver was designed
as part of a 3-cm radar set installed on small ocean-going vessels for sea-
search and navigational purposes. The receiver is built into a steel box
which fits into the r-f head. The general construction and layout can be
seen from Fig. 12T6. Separate AFC and signal mixers are incorporated
in the receiver; the choke joints for connection to the r-f system can be
seen in the side view. A shutter is shown across one of the waveguides in
the position it occupies when the transmitter is off. This shutter pro¬
vides crystal protection against signals picked up on the antenna when
the TR switch is not firing. At the other end of the receiver are a video¬
output jack and a terminal strip for bringing in power and certain control
voltages.

The local oscillator is a 723A/B klystron. It supplies r-f power to
both the AFC mixer and the signal mixer. Its frequency can be varied
over a wide range by mechanical tuning and over a smaller range by
varying the reflector voltage.

Except for the common local oscillator, the receiver is divided into
two portions, the AFC channel and the signal channel (see Fig. 12-17).
The latter consists of six i-f amplifier stages, a detector, and a video
stage. Each stage of i-f amplification uses a 6AC7 pentode with single-
tuned coupling circuits. All stages but the last have a 1200-ohm load
resistance, 1 giving a single-stage bandwidth of a little over 6 Mc/sec and
an over-all i-f bandwidth of nearly 2 Mc/sec. The nominal gain of the
l-f amplifier is 120 db. A 6H6 diode second detector is capacitively
coupled into a single video stage.

The video stage serves as a combined line driver and limiter. It
operates as a cathode follower, the cathode resistance of 100 ohms being
located at the end of the video line. The screen voltage is set at such a
value that the tube draws approximately 10 ma of current with no signal;
this puts 1 volt across the 100-ohm line. Negative signals from the
detector may drive the grid to cutoff, thereby reducing the cathode volt¬
age to zero. The video signals at the cathode are then negative and
limited to 1 volt in amplitude.

The gain of the i-f amplifier is adjusted by varying the voltage on the
grid of the second and third stages by means of an external control.

The receiver can be tuned either manually by means of an external
potentiometer, or automatically by means of a 5-tube AFC circuit.
The AFC circuit is of the hunt-lock type briefly described in Sec. 12-7.
The reflector of the 723A/B local oscillator is swept over a range of about
30 volts, the center of the range being set by the manual frequency

1 R-f chokes, self-resonant at 30 Mc/sec, are wound on the load resistors to reduce
the power dissipation in the resistor and to keep the plate voltage up to the screen

voltage.

-255v

Fig. 12-17.—Circuit of general-purpose receiver.

464 THE RECEIVING SYSTEM—RADAR RECEIVERS [Sec. 1210

control. The sweep voltage is generated by the 884 thyratron operating
as a relaxation oscillator. When the discriminator crossover point is
reached, positive pulses from the video amplifier Fn fire the gas tube Vn,
thus stopping the sweep.

To obtain the control pulses a very small part of the transmitter r-f
power is mixed with a portion of the local-oscillator output signal in the
AFC crystal. The beat frequency generated by the crystal is then
amplified by Fj and applied to the discriminator detector. The dis¬
criminator output signal, in the form of a video pulse, is amplified by Fu
before being applied to the control tube.

12-10. Lightweight Airborne Receiver. 1 —This receiver is part of a
lightweight 3-cm airborne radar (AN/APS-10) intended primarily for
navigation. It was designed to require a minimum of field test equip¬
ment and a minimum number of highly trained service personnel.
Accordingly, as far as possible the system was divided into small units
that coidd be replaced, rather than repaired, in the field.

The receiver is distributed among several subunits, which, except for
the video amplifiers, are enclosed (along with the r-f components, trans¬
mitter, modulator, and most of the power supplies) in a pressurized con¬
tainer forming one of the major units of the system. These subunits of
the receiver are the following:

1. A unit containing a double crystal, mounts for 723A/B radar and
beacon local oscillators, and a low-Q reference cavity for the beacon

.AFC.

2. An AFC unit for both radar and beacon local oscillators.

3. An i-f strip containing the entire i-f amplifier, the second detector,
and a video cathode follower.

4. Power supply.

The receiver supplies low-level video signals to either one or two cathode-
ray tubes, each of which is equipped with a video amplifier.

The i-f amplifier, a schematic view of which is shown in Fig. 12-18,
contains eight 6AK5 pentode tubes. Its construction is shown in Fig.
12-19. The input circuit is a ir-network consisting of three self-induct¬
ances. A crystal-current jack and decoupling filter are provided. The
first six tubes are i-f amplifiers whose interstage coupling networks are
single-tuned circuits arranged in two stagger-tuned triples. The center
frequencies of these circuits are, in order, 30.0, 33.7, 26.7, 33.7, 26.7, and
30.0 Mc/see, giving an average over-all i-f bandwidth of 5.5 Mc/sec
centered at 30 ± 1.5 Mc/sec. Fixed tuning is employed in this replace¬
able subunit. The i-f bandwidth is made considerably wider than that

1 By L. Y. Beers and R. L. Sinsheimer.

466

THE RECEIVING SYSTEM—RADAR RECEIVERS [Sec. 1210

necessary for the reception of the 0.5-Msec pulses employed by the system,
to allow for tolerances in the adjustment of the AFC unit and in the manu¬
facture of the i-f strip as well as for a slight spread in the frequencies of
beacons. The voltage gain between the grid of the first tube and the
plate of the sixth is about 30,000.

The seventh tube is a plate detector, which gives 10-db gain as well
as a somewhat larger power output than could have been obtained from a
diode detector of the same bandwidth. This advantage, however is

L._

Fig. 12-19.—AN/APS-10 receiver; top and bottom views.

accompanied by three disadvantages. First, this detector is not strictly
linear, a difficulty that is not too serious since this system is not intended
to be operated in situations where interference is to be encountered.
Second, with certain detector tubes there is some “blackout effect”—
that is, the sensitivity does not recover immediately after the transmitted
pulse or after other very strong signals. Third, care must be employed
in the design of the power supply to reduce plate-supply ripple because
such ripple is amplified by the entire video amplifier. The detector has
an output test point for convenience in checking the pass band.

The last tube is a cathode follower which supplies negative video

Sec. 1210]

LIGHTWEIGHT AIRBORNE RECEIVER

467

signals at 1-volt peak, through a 75-ohm line, to the video amplifiers at
the cathode-ray tubes. The half-power video bandwidth of the coupling
network between the detector and the cathode follower is 6 Mc/sec.

The noise figure determined from measuring approximately 100 such
amplifiers ranged from 1.7 to 4.5 db, with the average at 3.3 db. This
amplifier was designed before the development of the grounded-cathode
grounded-grid triode input circuit. The use of such an input circuit
would require one more tube or the equivalent thereof. As an experi¬
ment, one of the standard receivers was modified to use this input circuit,
the first seven tubes being in the i-f amplifier. The detector tube was
replaced by a 1X34 germanium crystal, which allowed the unit to be con¬

tained in the same chassis, though with some crowding. The noise
figure of this experimental amplifier was 1.6 db.

The amplifier is mounted on a 91 by 21-in. chassis, which permits easy
access to all components. The sides of the thin stainless steel cover are
held by special springs at the edge of the chassis. In order to obtain
stability, it was necessary to provide the chassis with two baffles to reduce
feedback. These consist of small pieces of sheet metal fastened to the
chassis and making contact with the. bottom of the cover. Good contact
between the bottom of the cover and the baffles is obtained by the use of
screws which pass through the cover and are tapped into the baffles.

The i-f strip requires a power supply giving 65 ma at +105 volts
unregulated for plates and screens, 1.4 amperes at 6.3 volts a-c for
heaters, and a voltage variable from 0 to —10 volts (with a source

468

THE RECEIVING SYSTEM—RADAR RECEIVERS [Sec. 1210

impedance not over 2000 ohms), which is applied to the control grids of
the second and third i-f stages to control the gain.

The video amplifiers for the cathode-ray tubes (Fig. 12-20) have two
stages and use 6AK5 tubes. The input signal is —1 volt peak; the
amplifier output supplies —30 volts peak to the cathode of the indicator
tube. The half-power bandwidth is 4 Mc/sec.

The chassis also contains a 6AL5 dual-diode tube. One half of this
tube is used in a circuit to lengthen the duration of beacon reply pulses
and so give a brighter spot on the CRT screen. On the rise of the pulse
the diode conducts, and the input capacity of the second tube is charged
rapidly. When the amplitude of the pulse starts to decrease, the diode
no longer conducts, and the charge on the grid of the second tube leaks
away slowly through a 2 . 2 -megohm resistor.

The other half of the 6AL5 is used as a d-c restorer for the cathode-ray
tube.

This amplifier is mounted on a chassis having the form of an annular
ring which fits around the neck of the cathode-ray tube. The power
supply requirements are 20 ma at +140 volts for plates and screens, and
0.5 amp at 6.3 volts for heaters.

Automatic-frequency-control Circuit .—The AFC subunit provides
automatic control of the radar and beacon local-oscillator frequencies.
The schematic view of the eight-tube circuit is shown in Fig. 12-21.

Both search and beacon AFC systems are of the search-and-lock type
(Sec. 12-7). A sawtooth generated by the recovery of the grid circuit
of a blocking oscillator, V 6 , sweeps the reflector voltage and thus the
frequency of a klystron. In radar operation, i-f signals from a separate
AFC crystal are amplified by Vi and applied to the discriminator formed
by V 2 and associated circuits, which is centered at 30 Mc/sec. The out¬
put pulses from the discriminator are amplified in F 3 and applied to the
grid of the thyratron V t . When the pulses change sign and become
positive at the crossover, they trigger the thyratron and stop the sweep
voltage.

In beacon operation, power is transferred from the search local
oscillator to the beacon local oscillator, which (as described in Sec. 12-7)
is coupled to the receiver crystal and to a reference cavity tuned to a
frequency 30 Mc/sec below the beacon frequency. A small 1000-cycle
sinusoidal modulation, supplied by oscillator Vs, is superimposed on the
sawtooth applied to the reflector. The output of the beacon crystal,
which is coupled to the local oscillator through the reference cavity, is
amplified in Fe and then applied to F 7 .

As explained in Sec. 12-7, the phase of the a-f amplitude modulation
of the signal from the beacon crystal will change by 180° when the fre¬
quency of the local oscillator crosses the center frequency of the reference

Sec. 1210] LIGHTWEIGHT AIRBORNE RECEIVER

470

THE RECEIVING SYSTEM—RADAR RECEIVERS [Sec. 1211

cavity. This phase shift is detected in the phase-comparison tube V
by applying the amplified crystal output to the control grid and the audio
oscillator output to the suppressor grid. Both grids are biased to cutoff,
so that no current flows in the tube unless the signals are in phase. The
circuit is so arranged that the 180° shift in phase of the audio signal pro¬
duces phase agreement, thereby providing pulses of plate current on
alternate half cycles of the audio signal. These pulses, further amplified
in F 3 , then trigger thyratron Vi to stop the sweep.

The change from search to beacon operation is performed remotely
by relays which switch the grid input to V 3 , switch from the reflector
voltage-control potentiometer P 1 to P 2 , change over the plate power
from the search to the beacon local oscillator, and superpose the sinusoidal
modulation on the sawtooth.

Switch Si enables a maintenance man to tune the local oscillators
manually to the proper frequencies for signal reception with Pi and P 2
(for the search or beacon local oscillators respectively), and then to
revert to AFC operation centered at the correct frequency. This switch
is spring-loaded so that the circuit cannot be left on manual tuning.

Jacks are provided at which the radar AFC crystal current and the
beacon AFC crystal current can be measured. A pin-jack test point is
provided at the grid of Fa to aid in aligning the discriminator, and another
at the plate of F 3 for checking the control signals to the thyratron.

This AFC unit requires a power source supplying 5 ma at +300 volts,
23.5 ma at +105 volts, 2 ma at —300 volts, 1.55 amp at 6.3 volts, and 0.8
amp at 6.3 volts at —225 volts from ground. None of these voltages
needs to be regulated, although the plate voltages must be well filtered.

1241. An Extremely Wideband Receiver. —The receiver shown in
Figs. 12-22 and 12-23 is a good example of a design for a receiver having a
very wide bandwidth. It was designed for a 3-cm radar system with a
0. 1 -gsec pulse width. In order to reproduce such short pulses and still
maintain a good signal-to-noise ratio, an i-f bandwidth of at least 10
Mc/sec is required; the bandwidth of the receiver is 12.5 Mc/sec.

The i-f amplifier consists of 12 stages, 6AK5 tubes being used in all
but the second. The intermediate frequency is 60 Mc/sec, the total
gain being approximately 120 db.

An intermediate frequency of 60 Mc/sec instead of 30 Mc/sec was
chosen for two reasons. First, fairly tight coupling is required between
the primary and secondary of the i-f transformers to attain wide band-
widths. It is easier to make this coupling tight at 60 Mc/sec than at
30 Mc/sec. Second, the AFC operation is more certain at the higher
frequency. The AFC circuit can lock the local oscillator on either side
of the transmitter, provided the local oscillator is producing power at
both frequencies. However, since the correct beat frequency is produced

Sec. 12-11] AN EXTREMELY WIDEBAND RECEIVER

472 THE RECEIVING SYSTEM—RADAR RECEIVERS [Sec. 121]

Sec. 1211]

AN EXTREMELY WIDEBAND RECEIVER

473

in only one of these cases, it is necessary for the local oscillator to cease
oscillating when it is on the “wrong” side of the transmitter frequency.
This can be counted on only when the intermediate frequency is high.

Double-tuned circuits were chosen in preference to stagger-tuned,
because it was felt that they would give a smaller change in the shape of
the response curve for a given change in tube capacity. The circuits were
loaded on both sides to reduce still further the sensitivity to tube-capacity
changes. Equal values of primary and secondary Q would have been
best in this respect; actually a compromise Q-ratio of 2.2 was adopted
to give a little more gain than equal Q’s would provide. The transformer
coils are wound adjacent to each other on a powdered-iron core to give
tight coupling. A thin spacer between the two coils is of such thickness
as to make the coupling just transitional. The gain per stage is approxi¬
mately 11 db, and the single-stage bandwidth 25 Mc/sec.

The 6AK5 tube is chosen in preference to the 6AC7 because it is
smaller, takes less power, and has a smaller variation in input and output
capacity. It also gives a better receiver noise figure when used in the
first stage. A 6J6 is used in the second stage because of its low plate-to-
cathode capacity, an important factor in grounded-grid triode operation.

The first two stages are operated as triodes; in spite of the high inter¬
mediate frequency and the broad bandwidth, an i-f noise figure of 3.5 db
can usually be attained.

Both signal and AFC mixers are of the balanced type. This effec¬
tively cancels out local-oscillator noise and provides good isolation
between the two channels. There are two crystals in each mixer, pro¬
vision being made for monitoring the current in each of the four crystals.

The local oscillator is a 2K25 klystron, which can be tuned mechani¬
cally over a large range and electrically over a restricted range of some
30 Mc/sec. The electrical tuning can be done manually, by means of a
remote potentiometer, or automatically.

The AFC circuit operates as follows. The beat frequency obtained
by mixing a small part of the transmitter power with local-oscillator
power is amplified by two i-f stages and then applied to the discriminator.
The video pulses from the discriminator undergo one stage of amplifica¬
tion before reaching the control tube, Vs (Fig. 12 23). Tube V e generates
a sawtooth sweep which moves the reflector voltage of the local oscillator
through a range determined by the setting of Ru] the sweep is stopped at
the correct voltage to receive signals by the firing of the control tube.

The video amplifier consists of a limiter-amplifier stage which drives a
cathode follower operating into a line terminated with 75 ohms. Limited
signals of 1.5 volts amplitude appear across the line. The video ampli¬
fier is very wide, the bandwidth of each stage being about 22 Mc/sec.
This bandwidth is obtained by means of a shunt-series peaking network

474 THE RECEIVING SYSTEM—RADAR RECEIVERS [Sec. 1211

which gives a gain-bandwidth product 2.4 times as great as that of a
simple RC circuit and still has only 0.3 per cent overshoot.

The limiter stage is operated with a low voltage (50 to 55 volts) on
the screen, which means that only 2 volts of signal is required to drive
the tube to cutoff. This reduces the amount of i-f gain required and
increases the ratio of the maximum obtainable signal to the video limit
level. During extended periods of high duty ratio the screen voltage
will increase, thereby increasing the height of the limited video-output

Fia. 12.24.—Receiver chassis of a very wideband receiver, bottom view.

signals. The rising screen voltage is checked at 60 volts by the diode

Tl36-

The layout of the receiver can be seen in Fig. 12-24. The i-f amplifier
is in the form of a long, narrow strip, folded, at one end. The coupling
transformers and associated components are laid in a channel which
becomes a tube when the cover is in place. Coupling between output
and input circuits is very small, since the tube acts as a waveguide
attenuator at the intermediate frequency. The mixer (not shown) is
attached to the top of the chassis directly behind the input coupling
transformers at the upper left of the picture. The AFC circuits occupy
the upper central portion of the chassis.

CHAPTER 13

THE RECEIVING SYSTEM—INDICATORS

By L. J. Haworth

THE CATHODE-RAY TUBE

The effectiveness of a cathode-ray tube as a radar indicator is influ¬
enced by a number of factors, among them: (1) the size of the tube face;
(2) the intensity of the emitted light, which is determined by both the
strength of the electron beam and the efficiency of the screen; (3) the
decay properties of the screen and the manner in which it integrates
repeated signals; (4) the resolution; (5) the grid-modulation characteris¬
tics; (6) the effect of the tube on the over-all complexity, weight, size, and
power dissipation of the complete indicating equipment.

These properties are not independent, and in many cases a compromise
among them must be reached. As a result of the variety of operational
demands a large number of types of tubes have been developed. The
next few sections describe some of their salient features.

13-1. Electrical Properties of Cathode-ray Tubes. —Cathode-ray
tubes are classified as “electrostatic” or “magnetic” in accordance with
the method of deflection. An example of each is given in Fig. 13T. The
electron beam originates in a hot cathode at the end of the tube remote
from the screen. In traversing the tube it is acted upon by a number of
electrostatic, or electrostatic and magnetic, fields which serve to control
and focus it.

The beam is collimated and controlled in intensity by the “control
grid,” a pierced diaphragm immediately in front of the flat oxide-coated
cathode. In most American tubes a “second grid” at a positive poten¬
tial of a few hundred volts serves to attract the electrons from the space
charge in much the same way as does the screen grid in an ordinary
tetrode or pentode. The electrons are given their final high velocity by
a potential difference of a few thousand volts maintained between
the cathode and an anode formed by a conducting coating of carbon
(Aquadag) on the inner surface of the glass at the screen end of the tube.

Focusing can be either electrostatic or magnetic. As indicated in
Fig. 13 T the same type of field is usually used for focusing and deflection
in a given tube. 1

'Occasionally electrostatic focusing is combined with magnetic deflection; such
tubes have not come into wide use in this country.

475

476

THE RECEIVING SYSTEM—INDICATORS

[Sec. 13-1

In electrostatically focused tubes a “focus electrode” (first anode)
between the second grid and the high voltage anode is maintained at an
intermediate potential. The various electrodes are so shaped that strong
electron lens actions are produced by the fields at the two gaps. Adjust¬
ment of focus is made by controlling the potential of the focus electrode.

Magnetic focusing is accomplished by means of a longitudinal mag¬
netic field of circular symmetry which increases in intensity from the
center to the edge of the tube and thus has radial components that help
provide the focusing action. External coils or permanent magnets are
used to produce this field.

Electrostatic deflection is accomplished by passing the beam between
two orthogonal pairs of deflecting electrodes or plates. The deflection
due to each pair is accurately proportional to the potential difference
between its members. The individual deflections due to the two pairs
of plates add vectorially. The deflection sensitivity at the screen
depends upon the geometry of the deflecting plates themselves, their
distance from the screen, and the velocity of the electrons as they pass
the plates. The two pairs are similar in geometry, but, since they are
at different distances from the screen, their deflection sensitivities are
unequal.

In the electrostatic tube shown, the electrons achieve their final
velocity before reaching the deflecting plates. In some tubes designed
for high-voltage use, deflection sensitivity is increased by applying

Sec. 13-1] ELECTRICAL PROPERTIES OF CATHODE-RAY TUBES 477

approximately half of the total voltage across a gap in the Aquadag at a
point beyond the plates. The two parts are then spoken of as the
"second anode” and “third anode.”

Any variation of the mean potential between either pair of plates has
a marked effect on the focus; consequently if good focus is important it is
necessary to use push-pull deflection. 1 Furthermore, it is best that the
mean potentials of the plates be close to that of the second anode. All

(c > (<f)

Fig. 13-2. —Deflection coils, (a) Air-core deflection coii with Jumped winding; (£>) air-
core deflection coil with semidistributed winding; (c) iron-core deflection coil with pie
windings; (d) motor-stator type of deflection coil.

these potentials are often made the same, but in many tubes it is profita¬
ble to provide an adjustment for making the first pair of plates slightly
more negative.

Magnetic deflection is accomplished by passing currents of the desired
waveforms through a coil or combination of coils surrounding the tube
neck (Fig. 13T). The deflection due to each coil is proportional to the
current through it, and the combined deflection is the vector sum of the
individual ones. A few of the coil geometries used are described below.

A single coil 2 is used in a rotating-coil PPI. Typical air-cored and

1 For the sake of simplicity this is not usually indicated in block diagrams.

* A coil usually consists of at least two separate windings symmetrically placed
with respect to the tube. They may be connected either in series or in parallel.

478

THE RECEIVING SYSTEM—INDICATORS

[Sec. 131

iron-cored coils for this purpose are sketched in Fig. 13-2 and pictured in
Fig. 13-3. Care must be taken that surrounding fixed objects do not
introduce a lack of rotational symmetry and that no magnetizable
material is included in the rotating parts.

Multiple coils are used for many different purposes. Their fields
must occupy the same axial region of the tube in order to avoid serious
defocusing and distortion which otherwise take place when deflections

(s)

Fig. L3-3.-—Deflection and focusing devices for magnetic CUT. (a) Square iron-core
deflection coil in case. (V> Square iron-core deflection coil, (c) Air-core deflection coil for
off-center PPI, used in conjunction with ( d ). (d) Off-centering coil, (e) Toroidal iron-

core deflection coil. (/) Air-core deflection coil with distributed windings, (g) Motor-stator
deflection coil. ( h) Permanent-magnet focusing unit. Focusing coil.

of appreciable magnitude are combined. In some applications requiring
a fixed component of field, a permanent magnet is used in lieu of a coil.

Often coils are arranged orthogonally (Fig. 13-3) either to produce
entirely independent deflections (as in a type B display), or to provide a
single radial deflection (such as a range sweep) by adding its two rectangu¬
lar components vectorially. The latter technique is used in the RHT, the
fixed-coil PPI, and in other applications.

It is sometimes necessary to add dissimilar deflections in the same
direction. Whenever practical, this is done by adding the various
deflecting currents in the same coil. Tn some cases, however, this is

Sec 13-2]

CATHODE-RAY TUBE SCREENS

479

wasteful of power—for example, when a steady deflection is to be added
to a high-frequency sweep that requires a coil of low inductance and there¬
fore low sensitivity. It is then worth while to use two separate coils or a
permanent magnet and a single coil. If two coils are used, they are
usually placed together (on the same yoke when iron is used), but in
extreme cases they must be separated to avoid interaction.

A rotating coil and a fixed coil can be used in combination—for
example, to produce an off-center PPI. The fixed coil is placed outside
of the rotating one, which must then contain no iron. The outer unit
may contain a single coil that can be manually oriented, or it may have
two orthogonal coils that can be separately excited. If the amount of
off-centering is to remain fixed, a permanent-magnet arrangement can
replace the outer coil.

In the specific design of the coils many factors must be considered.
They should be as economical of over-all power as possible. The mag¬
netic fields must be so shaped that they produce a linear deflection and
cause no harmful effects on focus. When multiple coils are used, it must
be possible to prevent harmful effects from interaction.

The current sensitivity of the coils should be made as high as prac¬
ticable since this minimizes power losses. For a given geometry, the
sensitivity is directly proportional to the number of turns, which should
therefore be as high as practicable. However, for a given rate of deflec¬
tion (i.e., a given rate of change of flux) the voltage induced in the coil is
directly proportional to the number of turns. This usually sets an upper
limit to the number of turns that can be used within the bounds of a
reasonable power supply voltage.

These and other matters pertaining to coil design are discussed at
length in Yol. 22 of the series.

13-2. Cathode-ray Tube Screens. Phosphorescent Screens .—The
important characteristics of the screen are its decay properties, its effi¬
ciency, and the manner in which it integrates or “builds up” on repeated
signals.

When scanning interrupts the picture, the screen must have sufficient
persistence (“afterglow”) to permit observations and measurements on
the echoes and in so far as possible to furnish a continuous picture. On
the other hand, the image must not persist so long as to cause confusion
on a changing picture. In terms of the scanning rate, three cases may
be considered:

1. Cases in which little or no persistence is needed, either because the
frame time is less than the retentivity time of the eye (about sec)
or because observations are made in the absence of scanning.
Screens incorporating the green willemite phosphor used in ordi-

480

THE RECEIVING SYSTEM—INDICATORS

[Sec. 13-2

nary oscilloscope tubes and known as type P-1 (phosphor number
1) are almost universally used in such applications. This material
has an exponential decay with a time constant of a few milli¬
seconds; it is extremely efficient in terms of light intensity.

2. Applications in which persistence is needed to smooth out the

effects of flicker. The best Ameri¬
can screen for this purpose, desig¬
nated P-12, utilizes a zinc-magnesium
fluoride phosphor which has an
exponential decay of time constant
between 60 and 100 msec (Fig. 13-4).
Because the response of the eye is
logarithmic, this screen is satisfac¬
tory for scanning rates as slow as a
few per second. On the other hand,
the exponential rate of decrease pre¬
vents anv long-time tailing-out and

0.001 0.01 0.1 1 10 in ' ,, . , ,

Time in sec consequent blurring of a changing

Fio. 13-4.—CRT screen characteristics. picture. The efficiency is somewhat

less than that of the P-1 screen.

3. Applications in which the scanning is so slow that considerable
persistence is needed to afford viewing time and to provide a com¬
posite picture. This classification covers scanning rates from a
few per second up to one or two pei; minute; it includes the bulk
of present-day radars with the exception of fire-control equipment.

Long-persistence phosphors have better buildup and decay properties
under weak excitation than under strong excitation. Unfortunately the
extremely thin layer penetrated by electrons of cathode-ray tube energies
must be strongly excited to provide enough total light. On the other
hand, if excitation by light could be used the excitation density could be
kept very low because the screen would be excited throughout. This is
accomplished by the simple but exceedingly clever expedient of cover¬
ing the persistent screen with a second layer of a blue-emitting phosphor
which undergoes primary excitation by the electrons. The blue light
from this layer in turn excites the persistent screen. This process
results in considerably lower over-all efficiencies than those of the single-
layer screens.

Two varieties of such “cascade” screens are commercially available
in this country. The P-14 is suitable for frame times up to a very few
seconds, and the P-7 has a much longer persistence (Fig. 13-4). The
persistent phosphors, which emit a predominantly yellow or orange light,
are composed of copper-activated zinc-cadmium sulphides, the zinc-

Sec. 13-2]

CATHODE-RAY TUBE SCREENS

481

cadium ratio governing the decay characteristics. The blue layer is
silver-activated zinc sulphide. Since its decay is very rapid, an orange
filter is customarily used to remove its “flash,” particularly at the faster
scanning rates.

The decay of these cascade screens is an inverse power rather than an
exponential function of the time, so that the disappearance of old signals
is less clean-cut than with the P-1 and P-12 types. Unfortunately no
phosphors with exponential decays of more than about 100-msec time
constant have as yet been developed.

It is difficult to obtain sufficient light from intensity-modulated dis¬
plays during scanning, since each point on the tube is excited only inter¬
mittently. The problem is especially acute on the slower scans, partly
because of the long time between excitations and partly because the
cascade screens are less efficient than those with less persistence.

In intensity-modulated displays the characteristics of the screen have
important effects on the signal-to-noise discernibility. As has been
pointed out in Chap. 2, the energy per pulse necessary for an echo to be
just discernible is inversely proportional to the square root of the number
of pulses included in the observation. From this standpoint the screen
should enable the operator to integrate or average over the maximum
number of pulse cycles consistent with other requirements; the intensity
of each spot should represent the average of all the excitations received
over a very long time in the past. The limits within which this can be
accomplished are set by the achievable properties of the screen, and by
the degree to which past information can be retained without causing
confusion as the picture changes.

The screen properties of importance in this connection are the type
of decay and the manner in which the light intensity “builds up” under
successive excitations. To examine their effects, consider first a scan
which is so slow that either the limitations of achievable persistence or
the requirements of freedom from display confusion due to target motion
prevent appreciable storage of information from one scan to the next.
In such a case, the averaging must be done over a single pulse group.
With modern narrow antenna beams and customary scanning rates the
time occupied by this group is always short compared with the total
scanning time and achievable decay times. The screen chosen should
have sufficient persistence so that there is no appreciable decay 1 during
the process of scanning across the target and the entire echo arc is observ¬
able at one time. In order that the average intensity of this arc shall
represent all of the data, it is essential that the screen integrate the effects
of all the pulses that overlap on a given focal spot—that is, it should not

'Except for that involved in the disappearance of the so-called “flash,” which
occurs for a very short time interval during and immediately after each excitation.

482

THE RECEIVING SYSTEM—INDICATORS

[Sec. 13-2

saturate too quickly. The number of overlapping pulses (which is
often large) is given for a PPI by the expression NS/oir at the center of
the arc, where N is the PRF, S is the spot size, u is the angular velocity
of the scan, and r is the distance from the origin of the display to the echo
spot. Thus for a 30-sec scan and a PRF of 400 (see Sec. 15-10) there
are about ten overlapping pulses at “ranges” corresponding to the
radius of a 7-in. tube, since S/r « The property of “building up”

in intensity because of excitation by successive members of such a group
of pulses is possessed to an adequate degree by all cascade screens, pro¬
viding the excitation is not at too high a level.

At faster scanning rates it becomes possible to provide screens having
carry-over from one scan to the next. Within the requirements set by
clarity in a changing picture, the longest obtainable persistence should
usually be used in order to average over the largest possible number of
pulses. However, the permissible decay time is so short in the case of
very rapid scans that the operator and not the screen has the longer
memory. The persistence should then be determined entirely by the
requirements of freedom from flicker on the one hand and freedom from
blurring due to motion on the other. 1 If a set has several indicators
involving different scale factors, their persistences should theoretically
be graded, fast screens being used on the expanded displays where the
picture changes rapidly and slower ones on those displays covering large
areas. Fortunately, it is usually the latter on which the signal-to-noise
discernibility is of most importance, since the expanded displays are
usually confined to near-by regions.

Providing the scanning is not too slow (for example, if it is approxi¬
mately one scan per second) certain types of cascade screens will, if
initially unexcited, display more than twice as much intensity after two
scans as after one, and so on, even though the intensity may have decayed
manyfold in the time between scans. This property of “supernormal”
buildup was at one time believed to be very desirable from the signal-
discernibility standpoint, on the hypothesis that it would give the
r epeating signal an advantage over random noise. However, the prop¬
erty is most exaggerated on an initially unexcited screen, whereas in
actual cases of successive scan integration the screen is initially excited
from previous scans. Furthermore, it is not evident a priori that the

1 When extended observations are to be made on a single target or region the
display is sometimes “frozen”; that is, the target motion relative to the radar is com¬
pensated so that the picture remains stationary. It is then possible to use longer
persistences without blurring. However, since observation of the frozen display is
usually part of the “tracking” operation which controls the removal of the motion,
the persistence must not be so long that it reduces the ease of detecting small changes
in target position.

Sec. 13-3]

SELECTION OF THE CATHODE-RAY TUBE

483

readjustment in the weighting of the successive pulse groups introduced
by this phenomenon is desirable. In any case, careful observation has
not detected any appreciable advantage for screens with very high super¬
normal buildup. The property of supernormal buildup may be con¬
nected, however, with other desirable ones. Indeed, those screens with
highest buildup are in general the ones that show the longest persistence.
These questions are discussed in detail in Vol. 22 of this series.

“Dark Trace” Screens .— Certain normally white salts, notably the
alkali halides such as KC1, have the property of darkening for a time at a
point where they have been struck by an electron beam of sufficient
energy. 1 This phenomenon has been made use of in one form of cathode-
raj r tube, known as the “skiatron” (screen type is P-IO) used for pro¬
jection purposes. By means of an intense external light source, opaque
projection of the tube face magnified several diameters is possible.
Although of value for this purpose, this type of screen has several dis¬
advantages. Contrast is always low, particularly if the duty ratio of the
pulses is low. Furthermore, such a screen has the unhappy property
that signals tend to “burn in” with time, which is a definite handicap
in a changing picture and is disastrous in the presence of certain forms of
interference. Except for the burning-in tendency, the normal persistence
is satisfactory through about the same scan intervals as is that of the
P-7 screen.

13-3. The Selection of the Cathode-ray Tube. —Both electrostatic
and magnetic tubes are available in various sizes and with various screens
(Table 13T). The most widely used wartime types are pictured in
Fig. 13-5. The following intercomparison of existing designs of electro¬
static and magnetic tubes can be made.

1. At the excitation levels necessary for intensity-modulated displays,
magnetic tubes provide much better focus than do the electrostatic
types. It is possible to resolve about 175 to 200 fairly intense spots
along the radius of most magnetic tubes, whereas the figure for
electrostatic tubes is more like 75 to 100. On the other hand, at
the lower beam currents needed for deflection modulation, the
electrostatic tubes perform very well.

2. Magnetic tubes are more costly to deflect than electrostatic tubes,
particularly at high frequencies. Xo attempt is made to deflect
magnetic tubes at video frequencies.

3. Electrostatic tubes are, in general, much longer than the equivalent
magnetic tubes, but the size, weight, and power dissipation of the
over-all equipment is greater with magnetic tubes, partly because
of the weight of the focusing and deflecting mechanisms and partly

1 See Chap, 18, Vol. 22 of the series.

I'ig. 13 5.—Representative electrostatic cathode-ray tubes: (a) 5BP1, (5) 5CP1, (c)
3JP1, (d) 2AP1. Representative magnetic cathode-ray tubes: (e) 3HP7, (/) 4AP10,
Co) 51' Pr, Ch) rBP7, (i) 12DP7. Most of these tubes are available with other screen types.

Sec. 13-3]

SELECTION OF THE CATHODE-RAY TUBE

485

because of the greater power required for deflection. These
differences are of significance only in airborne equipment.

4. The grid-modulation characteristic of most electrostatic tubes
follows approximately a square law, whereas that of the guns used
in most magnetic tubes is cubic. As compared with a linear
response, these characteristics have the unfortunate property of
lowering the dynamic range of usable echo intensities since they
reduce the ratio between the upper limit of useful signal swing,
set by the tendency to defocus, and the level below which the
intensity is insufficient.

Table 13-1.—Cathode-ray Tubes Commonly Used-for Radar Applications

Max. acceler-

ating voltage

Useful

(nominal)

Specified

Bulb

diam-

Type of

maximum

Commonly

number

eter,

deflection

Posh

spot diam-

used screens

in.

Anode

deflec-

eter, mm*

tion

anode

1.75

Electrostatic

1000

0.5 to 0.6

p-i

2B (New)

1.75

Electrostatic

2500

p-i

2.75

Electrostatic

2000

0.55 to 0.75

p-i

3D (Central

2.75

Electrostatic

2000

0.6 to 1.0

electrode)

2.75

Electrostatic

2000

4000

P-7

2.75

Electrostatic

2000

4000

0.75 to 0.9

P-1, P-7

2.5

Magnetic

5000

0.5 to 0.6

P-7, P-12, P-14

3.38

Magnetic

9000

0.3

P-10

4.5

Electrostatic

2000

0.6 to 1.0

P-1

4.5

Electrostatic

2000

4000

0.6 to 0.9

P-1, P-7, P-12, P-14

4.25

Magnetic

7000

0.5 to 0.6

P-7, P-12, P-14

4.5

Electrostatic

2000

4000

P-1, P-7

6.0

Magnetic

7000

0.75 to 0.85

P-7, P-12, P-14

7.62

Magnetic

7000

1.0 to 1.2

P-7, P-12, P-14

12G

10.0

Electrostatic

4000

6000

1.2 to 1.8

P-1, P-7

12D

10.0

Magnetic

7000

1.35 to 1.5

P-7

♦ Most magnetic tubes actually give from 0.5 to 0.7 of this maximum Bpot size. Electrostatic tubes
are in general near the maximum.

As a result of these factors, electrostatic tubes are invariably used for
deflection-modulated indicators, but, except in cases of extreme weight
limitation, magnetic tubes are used for most intensity-modulated displays.

The size of the tube selected depends upon the particular application.
The relative resolution is fairly independent of the size, so that from this
standpoint alone there is little value in increasing the screen diameter

486

THE RECEIVING SYSTEM—INDICATORS

[Skc. 134

beyond the point where the resolving power of the eye ceases to be the
limiting factor (5- to 7-in. magnetic tubes, 3- to 5-in. electrostatic tubes).
On the other hand, if geometrical measurements or estimates are to be
made, or if plotting is to be done, it is desirable to have as much dis¬
persion as possible; for such use the larger sizes are definitely preferable.
This requirement must be balanced against the available space, particu¬
larly in airborne equipment.

For many purposes even the largest available tubes (12-in. diameter)
are still too small, and it is desirable to provide an enlarged presentation.
Since at most scanning rates phosphorescent screens do not provide
enough light for projection, it is necessary to devise special methods. Of
those used to date, one involves the projection of a photograph of the
PPI or other scope, which is developed and projected in a few seconds by
special techniques; the other involves opaque projection from the skiatron
screen (see Sec. 7-3).

COORDINATION WITH THE SCANNER

Under various circumstances several different sorts of electrical
information must be delivered from the scanner to the indicator. (Some
of these have already been illustrated in Sec. 12T.)

1. Signals capable of controlling an electromechanical repeater. The
repeater can be used to position a cathode-rav-tube coil or to
provide a dummy scanner shaft to which the final data trans¬
mitters are attached.

2. Slowly varying voltage proportional to the scan angle, to be used
in the cartesian display of angle as in type B and type C displays.
The voltages can be obtained directly from a potentiometer of
proper characteristics or from the envelope of a carrier which has
been properly modulated. In many cases where the angle dis¬
played is small, sin 9 can be substituted for 6.

3. Signals produced by passing a range sweep voltage (or current)
through a resolver to produce an electronic PPI or an RHI.

4. Slowly varying voltages proportional respectively to the sine and
cosine of the scanner angle, which are used to control sawtooth
generators in such a way that they produce sweep components
equivalent to (3). This is spoken of as “ pre-time-basc ” resolu¬
tion. The voltages themselves can be transmitted by a poten¬
tiometer, or a modulated carrier can be used as in (2). The
approximations sin 9 — 6 and cos 6 ~ 1 are often used.

13-4. Angle-data Transmitters. —The devices that provide the
scanner data are known as “(angle) data transmitters.” They in-

Sec. 13-4]

ANGLE-DATA TRANSMITTERS

487

elude potentiometers, variable transformers, variable condensers, and
generators.

Potentiometers .—Potentiometers are principally used to provide
voltages whose only frequency components are those resulting from the
scanning. Because even the best potentiometers have a certain amount
of brush “jitter” which can be removed only by filtering, they are not
very satisfactory for resolving range sweeps. A wide variety of linear
potentiometers differing in accuracy, size, ruggedness, and so on have
been developed specifically for radar use (see Yol. 17). 1 For many pur¬
poses they provide the simplest method of data transmission and often
they are more effective than any other device. A difficulty arises,
however, in those cases where it is necessary to shift the sector under
view. This can be done within limits by adding a fixed voltage to the
circuit, but over any extended angle it is necessary to introduce the shift
mechanically by using a differential gear or by rotating the body of
the potentiometer. This requires either that the potentiometer be near
the operator or that a remote mechanical control be provided. Since the
second method is costly, some other data-transmission system is usually
chosen in preference.

Several varieties of potentiometer have been made with sine or with
sine and cosine characteristics, for use as resolvers (Vol. 17). These have
been designed with great care and are fairly good at low turning rates
and low signal frequencies. As data transmitters they are occasionally
used for purposes of pre-time-base resolution on slowly scanning systems,
or as a basis of information for computers.

Variable Transformers ( Resolvers , Synchros, etc .).—Figure 13-6a illus¬
trates the principle of certain variable transformers called “resolvers,”
“synchros,” “selsyns,” “autosyns,” and so on, which are widely used
as position-data transmitters. An iron-cored coil (rotor) of special shape
is mounted on a freely turning axis inside a slotted-iron framework much
like a motor stator. Two or three stator coils are symmetrically wound
into the slots in such a W'ay that the coupling of each with the rotor is
proportional to the sine of the rotor angle measured with respect to a
position of zero coupling. The device thus fulfills the requirements of a
resolver for a-c signals. An important aspect of this process is that the
polarity of the output signal at a given phase of the input signal reverses
as the synchro passes through a null position for that particular secondary
winding.

If the stators of an excited resolver, called the “transmitter,” are
loaded with the stators of a second, called the “repeater ” or the “receiver,”
(Fig. 13-66) the latter will experience currents producing a changing

1 Many of these potentiometers are useful as control elements for purposes other
than scanner-data transmission.

488

THE RECEIVING SYSTEM—INDICATORS

[Sec. 13-4

magnetic field in the same direction as the magnetic axis of the trans¬
mitter rotor coil. There will be induced in the receiver rotor a voltage
proportional to V sin (&i — 0 2 ) where &i and 82 are the respective orien¬
tations of the two rotors. If the receiver is provided with a second rotor
coil orthogonal to the first, it will experience a voltage proportional to
V cos (Si — d 2 ). Thus the two devices together “resolve” the original
voltage in terms of the difference of the two angles. A resolver with a
multiple-phase rotor is known as a “differential” synchro or resolver.
It is used in reducing data from relative to true bearing (one synchro

Fiq. 13*6.—Two-phase synchros, (a) Two-phase synchro; ( b ) differential synchro resolver.

being driven by a compass), and in enabling an operator to shift the
scanner reference angle for purposes of sector selection.

The 2-phase resolver has been used in nearly all practical applications
of the resolved-sweep technique to “electronic” PPI’s and RHI’s (Fig.
12-3) and in many applications where pre-time-base resolution is applied
to these displays.

For many purposes a 3-phase rather than a 2-phase 1 device is used.
If equal loads are applied across the three phases the sum of currents in
the three stators is zero. Thus, if this restriction is imposed, three brushes
and three wires can be eliminated by making a Y connection. If a
synchro with a 2-phase rotor is used as a receiver, its induced voltages
1 In this sense the word "phase” refers to rotation of the rotor rather than to the
internal phase of any signal being transmitted.

Sec. 13-4]

ANGLE-DATA TRANSMITTERS

489

will be proportional to the sine and to the cosine of the difference of the
two angles, as in the 2-phase case. If a 3-phase rotor is used, the machine
becomes a “differential,” which effectively subtracts the two angles in
developing its output voltages.

Three-phase synchros are widely used in mechanical repeaters. As
resolvers where the voltage itself is to be used, they have the disadvantage
that they do not deliver rectangular “components.” If only one com¬
ponent is needed, however, as in a type B or type C display (using the
approximation sin 9^8) they are often used because of their somewhat
higher accuracy and their greater availability.

Variable Condensers .—Certain types of rapid scanners (see Secs.
9-14 to 916) operate in such a way that, as a driving shaft rotates con¬
tinuously, the antenna beam scans
linearly across a given sector and
then ‘ ‘ snaps ’ ’ back and repeats itself.
Rotating - coil - indicator techniques
cannot be used in such applications;
hence the display must be synthe¬
sized electrically. The form of signal
modulation provided by a synchro
is suitable only for those sector
widths for which the discontinuity
in the scan can be achieved by
switching between stator leads (that
is, 90°, 180°, etc. for a 2-phase, 120°
for a 3-phase synchro). Poten¬
tiometers cannot be used for rapid
scans, since brush “chatter” becomes
excessive and the life is exceedingly
short. To fill this need, special
variable condensers have been devel¬
oped. An example of such a con¬
denser and one type of circuit used is
shown in Fig. 13-7. The condenser
plates are so shaped that the capacity increases as the rotor turns clock¬
wise, producing the desired potential variation (usually linear with angle)
across CV Recycling takes place when the rotor passes through the sector
in which there is no stator. The shaft is geared in such a way that the
condenser rotates 360° during one scanning cycle. Since C is never zero,
the output voltage has a constant term which must be removed in some
way.

In addition to specially shaped condensers such as that of Fig. 13-7,
more conventional ones are sometimes used with rapid scanners, in order

490 THE RECEIVING SYSTEM—INDICATORS [Sec. 13 5

to permit the use of higher carrier frequencies than can readily be passed
through a synchro.

Generators .—In some instances of conical or spiral scanning, part of
the scanner data is provided by means of a d-c excited 2-phase generator
geared directly to the scanner axis. In the case of conical scanning, the
output voltages of this generator are direct measures of the sine and
cosine of the phase of the scan. In the spiral scan, the voltages are
modulated in terms of the nod angle, either by varying the generator
field current by a potentiometer on the nod shaft, or by passing each
sinusoidal voltage through such a potentiometer after generation. The
signals thus produced can be used directly in the synthesis of type B and
type C displays.

13-6. Electromechanical Repeaters. —Two types of electromechanical
devices are used to repeat the motion of a rotating shaft at a remote
point.

The Synchro-driven Repeater .—If the stators and rotors are attached
respectively in parallel and the rotors are connected to an a-c power
source (Fig. 13-8), the two rotors will tend to align themselves in the
same direction. Any departure from this condition will result in cir¬
culating currents in the stators which will cause a motor action tending
to produce alignment. If one rotor is driven, the other will follow, with
only enough lag to furnish the necessary power. If the second rotor has
little or no mechanical load, this lag will be very small at rotational speeds
up to a few revolutions per second; if the load is appreciable, the lag may
amount to a few degrees. In order to reduce the effect of lag, the system
is often “geared up.” For example, the transmitter synchro can be
attached to a shaft rotating 10 times as fast as the scanner, and the receiv¬
ing synchro can then drive a rotating PPI deflection coil through a
10-to-l gear reduction. Under these conditions, the lag error can be
kept to a small fraction of a degree. There is, however, a 10-fold uncer¬
tainty in the position of the deflection coil in our example, since any of
10 antenna positions looks the same to the receiver. The necessity for
phasing the system manually each time it is turned on can be avoided

Sec. 13-5]

ELECTROMECHANICAL REPEATERS

491

either by a system of cams and microswitches which disables the repeater
when it is in any but the correct 36° sector, or in more elaborate ways.

Standard-design low-impedance synchros are used. Transmitter
and repeater are identical except for the inclusion of a mechanical damper
on the shaft of the repeater. The maximum speed of rotation of the
synchros is about 400 rpm, restricting a 10-speed system to 40 rpm.

The principal disadvantage of using synchros to provide torque is
that power must be transmitted by the primary synchro. This limits
the number of repeaters which can be used. Further, in systems with
more than one repeater, an error in any tends to throw the system off
balance and to affect the accuracy of other repeaters.

The Servomechanism .—Scanner position can be repeated at a distance
with an angular error as small as desired by means of a servomechanism.

This term refers to a device that is arranged to reduce to zero an “error
signal” present when misalignment between transmitter and repeater
exists. Synchros can be used to generate such an error signal. The
stators of the synchros are connected in parallel as before, with, perhaps,
a differential synchro inserted between them (Fig. 13-9) to allow compass
or other corrections. Only the transmitter rotor is excited from the line.
If the two rotors are oriented at right angles to one another, no voltage
is induced on the receiver rotor. Any departure from this orientation
results in an error signal whose internal phase is opposite for errors of
opposite sign. This error signal is amplified by vacuum-tube circuits
and used to drive the motor that turns the load. Proper phasing is deter¬
mined by reference to the line voltage, usually by using the latter to
provide field current for the motor.

As in the double-synchro direct-drive system, “gearing up” is often
used. Here, however, the proper rotational phase is usually selected by

492

THE RECEIVING SYSTEM—INDICATORS

[Sec. 13-6

a second servomechanism acting at “single speed.’’ Some sort of switch,
such as a gas-filled tube, serves to transfer control to the single-speed unit
when the error becomes large enough to confuse the higher-speed servo.

For further information on the extensive subject of electromechanical
repeaters, the reader is referred to Vol. 21 of this series.

BASIC ELECTRICAL CIRCUITS

The technique of producing radar displays involves the use of many
unfamiliar or entirely new types of vacuum-tube circuits. A great many
of these use a tube as a nonlinear element in such devices as electronic
switches, pulse formers, generators of rectangular and other waveforms,
etc. The following sections will describe briefly some of these techniques
in order to provide a basis for understanding the methods of display
production.

13-6. Amplifiers.— Xo attempt will be made here to describe the
standard forms of amplifier met with in ordinary vacuum-tube circuit

E in ~0Eoul

Fiq. 13-10.—Negative feedback principle.

the amplifier is then given by F ln
expressed as

Eout — (-Fin

practice, but a number of special
forms important in indicator de¬
sign will be touched upon. 1 The
important case of video amplifiers
has already been met in Sec. 12-6.

Negative Feedback .—In a large
number of instances negative feed¬
back is necessary to insure linear¬
ity and adequate frequency
response. The principles involved
are illustrated in the upper dia¬
gram of Fig- 13-10. By any of
several methods a fraction /3 of the
output signal is subtracted from
the input signal ahead of the
amplifier. The effective signal to
/SFcn. The output signal can be

/3F„„ t )Go,

where Go is the gain of the amplifier proper, in the absence of feedback.
Solving for E oa t,

_ G&F,n .

jSG 0 + 1 ’

1 For a complete discussion of amplifiers see Vol. 18 of this series.

Sec. 13-6) AMPLIFIERS

whence the gain of the entire device is

493

_ -S'out G0 1

" E lu - 0Go + 1 “ 7~T‘ W

P+ Go

If /3 is large compared to 1/Go, variations in Go will have little effect
on G. Care must be taken, in using large values of Go and /3, that phase
shifts in some of the frequency components do not result in positive feed¬
back and hence distortion or even oscillation.

The more usual method of representing the circuit is shown in the
lower diagram of Fig. 13-10, where the adding and amplifying are indi¬
cated together.

Fio. 13-11.—Cathode feedback, (a) General case; (6) cathode followers; (c) cable-matching.

Several types of negative-feedback amplifiers are used in indicator
circuits.

Cathode Feedback.-—A simple variety of negative-feedback circuit uses
an unbypassed cathode resistor to provide the feedback voltage (Fig.
13-lla). The load may be in the plate, it may be the cathode resistor,
or it may be divided between plate and cathode circuits to provide two
output points.

For a plate load, the feedback voltage is actually proportional to the
current through the load 1 rather than to the voltage across it; this is called
“current feedback.” If the load current is of interest (as in driving a
deflection coil), this is just what is wanted. If, on the other hand, the
voltage across the plate load is of interest, a cathode resistor gives the
proper type of feedback only if the load is also purely resistive. If

1 If a pentode or beam-power tube is used, the screen current passes through the
cathode resistor but not through the load. In very exacting cases some account
must be taken of this fact.

494 THE RECEIVING SYSTEM—INDICATORS [Sec. 13-6

the plate load is reactive, the cathode impedance should be also, with the
same sort of frequency response. For pure resistances the feedback
ratio is Ric/(Rl) and Go is Ri/(Rk + Rl) multiplied by the gain that
would obtain if both resistances were in the plate circuit.

In the cathode followers of Fig. 13-116, the cathode circuit serves as
the load and the plate is connected directly to B+, resulting in a nega¬
tive-feedback amplifier of gain less than 1, characterized by great linear¬
ity, excellent frequency response, high input impedance, and low output
impedance.

Since the entire output voltage appears across the cathode, the feed¬
back ratio /3 is unity. Therefore G is always less than 1 [Eq. (1)],
approaching, for large values of the cathode resistor, the value m/(m + 1),
where m is the voltage amplification constant of the tube. Since 1/G 0 is
nearly always considerably less than /3, the amplifier has a faithful
response.

The internal impedance of the circuit driving the total load is given

by - r~mr’ where g m is the mutual conductance and R p the plate

g m + 1/fip

resistance of the tube. This is a little less than 1 /g m , and is therefore in
the range from one to a few hundred ohms.

The input impedance of the tube itself (assuming no grid current)
results from the sum of the capacities between the grid and the fixed
elements (plate, screen, etc.), plus the grid-cathode capacity divided by
1 — G, where G is the gain. This impedance is in parallel with the grid
resistor and the wiring capacity. The effective impedance of the grid
resistor connection can be increased by the method shown on the right
in Fig. 13-116, since the drop in the grid resistor is thereby reduced.

Among the applications of the cathode follower are the following:

1. As a low-impedance source to supply the considerable power
required to drive such a load as a transformer or a deflection coil.

2. As a low-impedance source which will provide fairly uniform fre¬
quency response even when considerable capacity is associated
with the load. The time constant and therefore the high-frequency
response will be determined by the capacity in parallel with the
internal impedance of the tube and resistance Rh . Since the tube
impedance is small, good response can be obtained at frequencies
of a few megacycles per second, even with fairly large load capaci¬
ties. However, the internal impedance of the tube at any instant
depends upon the actual tube constants at that instant. A steep
negative wavefront may cause the grid to enter into a region of low
g m or to cut off, if the current flowing is too small to discharge the
oondenser with sufficient rapidity. The current can be increased

Sec. 13-6]

AMPLIFIERS

495

by using a smaller value of Rk, which sacrifices gain, or by using a.
positive grid bias. The latter is usually to be preferred.

3. To match the impedance of a cable. In this use the cable sees Rk
in parallel with the internal impedance of the circuit proper.
Correct methods of matching are shown in Fig. 13Tic.

Another special case of Fig. 13Tla is one in which the plate and
cathode resistors are made equal, thus providing equal signals of both
polarities from a unipolar input signal. Since the feedback ratio is unity
for each output signal, this “split load” or “phase-splitting” amplifier has
many of the desirable properties of the cathode follower, but the single¬
sided gain is always less and the internal impedance is greater.

Amplifiers for Deflection-coil Currents .—Special problems are involved
in producing rapidly changing deflection currents such as those involved
in range sweeps, since the voltage across the coil may become very large.
For a linearly increasing current (as in a range sweep) this voltage is
given by

L % + Ri = L % + Rat,
at at

where a is a constant. Since di/dt is also a constant the waveform con¬
sists of a step plus a linear increase. The sweep is usually produced by
an increasing current since, except in special cases, this results in the
minimum average current. As a result, the coil voltage drop during
the sweep results in a decrease in the plate potential of the driver tube.
The drop across the coil reaches its greatest value at the end of the fastest
sweep, and the power-supply potential must be designed to accommodate
this case. Such a sweep need not dissipate much power since the average
current is low, but unfortunately the same power supply is used on high-
duty-ratio sweeps where the average current is high. The total power
dissipation due to the sweep circuit can be minimized by using a large
number of turns on the deflecting coil and a correspondingly high supply
voltage, since this reduces the losses in the driver tube and in the power
supply itself. Usually, however, other circuits derive their power from
the same supply, and a high voltage results in unnecessary dissipation in
them. In consequence, the system is often designed in such a way that
the plate of the driver tube operates on the margin of insufficient voltage
on fast sweeps. Even if this were not the case, the amplifier would
tend to discriminate against the higher frequencies because of the higher
impedance offered by the coils to these frequencies.

As a result of these factors good range sweeps can be obtained only
with the use of greater negative feedback than would be necessary
merely to correct for nonlinearities in the tube in a normal application.

496

THE RECEIVING SYSTEM—INDICATORS

[Sec. 13 7

Special amplifiers satisfying these requirements will be described later
in connection with specific applications. Many of these employ multi¬
stage feedback.

13-7. The Generation of Rectangular Waveforms. —A rectangular
waveform is one whose outstanding characteristics are steep, alternately
positive and negative wavefronts with a space between (for example,
Fig. 13-12). The term will include waveforms whose “tops” and
“bottoms” are not completely flat.

In some applications only the timing of one or both wavefronts
matters, the particular shape of the whole wave not being of interest;

(a) Square wave oscillator
(no external stimulus)

(6) Flip-flop

f Trigger L
j Response

J_L

Sinusoid

(d) Flop over

Response J

Trigger #1 _L

Trigger #2 1 _ [

Response

(e) Scale of two

Trigger I I I

J_L

Response

Fio. 13-12.—Response of various waveform generators.

in others the shape is also important. Among the latter are such appli¬
cations as the intensifying of cathode-ray tubes and the operating of
various electronic switches. Rectangular waves can be used for timing
purposes—for example, to initiate the generation of sharp pulses or other¬
wise to initiate some particular event at the instant of occurrence of one
of the wavefronts.

The circuits that produce such waveforms can be divided into three
categories:

1. Those in which the waveform is produced without external
stimulus—that is, free-running oscillators (Fig. 13-13).

2. Those in which an externally induced departure from a stable state
with production of a wavefront is later followed by a spontaneous
return which produces the wavefront of opposite polarity (Fig.
13-14). Such a device is called a “single stroke” generator or

Sec. 13-7] GENERATION OF RECTANGULAR WAVEFORMS

497

“flip-flop.” It has wide application both in cases where the wave¬
form is directly used and in timing or “delay” circuits.

3. Those in which both wavefronts are externally induced. In this
class are the “squaring amplifier,” which produces square waves
from sinusoids or other waveforms, and various triggered devices.
The latter can be divided into two classes: (a) the “flopover” or
“lockover,” in which an external signal induces a change from one
stable state to another, and a reverse signal or one from a second
source reverses the operation (Fig. 1315a); and ( b ) “scale-of-two”
circuits, in which successive triggers from a single source induce
alternate transitions between two stable states (Fig. 13T56). The
name “scale-of-two” arises from the fact that if sharp pulses are
derived from those wavefronts of one polarity their number will be
half that of the original trigger pulses.

Fig. 13-13.—Eccles-Jordan multivibrator.

Aside from the squaring amplifier, which will not be discussed here,
there are three principal forms of rectangular-wave generators.

The Eccles-Jordan Circuit .—Figures 1313 to 13-15 illustrate a group
of two-tube circuits in which the sharp transitions are produced by posi¬
tive feedback from each plate to the alternate grid. All are based upon
a circuit of Eccles and Jordan. 1

Figure 13-13 illustrates the free-running multivibrator, which is a
form of relaxation oscillator. In order to understand its action, assume
an initial condition (for example, at t 0 on the waveform diagram) with
the grid of Vi beyond cutoff and that of V 2 at cathode potential. Then
Vi is temporarily quiescent with its plate at a low value; the plate of Vi
is at B+, and grid g i is rising exponentially toward bias potential as C i
is discharged through R\. At time h, gi reaches the cutoff point and Vi
starts to amplify. The amplified signal is passed to V 2 where it is further
amplified and fed back to V 1 . This regenerative action quickly lifts g 1
to the grid-current point and drives g? far past cutoff so that the original
condition is reversed. The plate of Vi is down and that of Vi is at B + .

1 W. H. Eccles and F. W, Jordan, Radio Rev., 1, 143 (1919).

498

THE RECEIVING SYSTEM—INDICATORS

[Sec. 13-7

Grid g 2 now rises, until at t 2 it reaches cutoff and regeneration occurs in
the reverse direction, and so on. Thus two square waves of opposite
phase are available from the two plates. For given tube types and
supply potentials, the time interval <1 — l 2 is primarily determined by
R 2 C 2 , and the time interval t 2 - t\ by R 1 C 1 ; these furnish convenient
constants by means of which control of the time intervals can be exerted. 1
The multivibrator can be used as a completely free oscillator, or it can be
synchronized by supplying it with a sine wave or a pulse train at a higher
frequency than that of the natural oscillation.

Figure 13T4 shows a single-stroke or “flip-flop” multivibrator.
The resistors and the bias voltage of the grid of V 2 are so chosen that
when Vi is fully conducting, </ 2 comes to equilibrium beyond cutoff; but
when Vi is cut off, g 2 is pulled-hard against the cathode. If left to its

(1) Trigger ~1 I I

*31 _ _ t_ 1_r-^Ground

(2) Grid 1 X /' Cuton

(3) Plate 1

(4) Grid 2

(5) Plate 2

_n_r

-r-f-p-T-

T_n_rL_r

-- Ground
Cutoff

B +

Fig. 13-14. —Eccles-Jordan flip-flop.

own devices, the circuit will come to equilibrium with IT on and V 2 off.
When an impulse of the correct polarity is applied to g 1 or to g 2 , the
regenerative action cuts off V\ and turns F 2 full on. Grid gi then rises
until the cutoff point is reached, when the regeneration reverses and the
cycle is completed with the original condition restored. The length of
the square pulse during the flip-flop action can be easily controlled by
varying RiC\ or the potential applied to R 1 . This voltage is made posi¬
tive to assure that g 1 will be rising sharply when the cutoff point is
reached; this helps maintain'a constant square-wave duration. Typical
circuit constants are indicated in the grid circuit of V 2 . The condenser
C 2 serves only to quicken the regenerative action and is not essential
except for the highest speed operation.

The “flopover” and the “scale-of-two” (Fig. 1315) are direct-coupled
in both directions in such a way as to have two stable states, and will
remain in either until disturbed in the proper manner. In the flopover,

1 For simplicity it can be assumed, as is practically always the case, that the supply
voltage is much higher than the cutoff voltage and that the plate resistors are much
smaller than the grid resistors but large enough to absorb most of the potential drop
when in series with a saturated tube.

Sec. 13-7] GENERATION OF RECTANGULAR WAVEFORMS

499

triggering signals from different sources, applied to the opposite sides,
result in opposite actions. Regardless of the order in which pulses are
received from the two triggering sources, the flopover will respond alter¬
nately to triggers from the two.

Fig. 1315.—Double external triggering of Eccles-Jordan circuits, (a) Flopover; (6)

scale-of-two.

In the scale-of-two, pulses from a single source are applied to both
sides; whenever a pulse arrives the circuit changes from one stable state
to the other. Thus two pulses are required to complete a full cycle.
The output waveforms can be used directly for switching purposes, or
they can serve as a means of generating pulses of half the frequency of
the original ones.

In all the above circuits it is feasible to use
self-biasing, but care must be taken that the
bias voltage is independent of duty ratio.

This can be assured by using a common self¬
bias resistor for both tubes, provided their
loads are the same.

Cathode-coupled Multivibrator .—F i g u r e
1316 illustrates a different type of single¬
stroke multivibrator which is considerably
better than the Eccles-Jordan variety for
accurate timing purposes. The two cathodes
are coupled through a common resistor, and plate-grid coupling is used
in one direction only. In the normal state, V 2 is conducting by virtue
of the positive grid supply voltage. The resulting current produces
sufficient potential drop across R k to cut off V 1 . If, now, a positive
trigger pulse of sufficient voltage is applied to gi (or a negative pulse to g 2 )
the amplified pulse is applied to V 2 through C, and V 2 starts to cut off.

Fig. 13-16.—Cathode-coupled
flip-flop circuit.

500

THE RECEIVING SYSTEM-INDICATORS

[StA 13-7

The drop in its current further reduces the bias on Fi, and there is a
violent regeneration which ends with F 1 full on and the grid of V 2 far past
cutoff. The grid of V 2 then experiences an exponential recovery toward
B+, and when the cutoff point is reached regeneration occurs in the
opposite direction and restores the initial condition. The circuit has the
marked advantage that the time for the flip-flop action is remarkably
linear with the bias voltage of g 1 , so that by means of an accurate poten¬
tiometer controlling this voltage a linear timing circuit of rather low
precision can be made. The circuit can be somewhat improved over that
shown in Fig. 13-16 by the addition of a biased diode in the grid circuit of
F 2 to determine the precise limit of the negative excursion of that grid.

Fig. 13-17.—Phantastron delay circuit.

The cathode-coupled multivibrator can also be used in the form of a
freely running oscillator, a flopover, or a scale-of-two, but the Eccles-
Jordan form is most common for such purposes.

The Phantastron —-The phantastron of Fig. 13-17 is a flip-flop of a
quite different type which serves as a timing circuit maintaining its
calibration to about one per cent. In the normal condition, Fi is
quiescent, with the cathode sufficiently positive to cut off the second
control grid so that all of the current goes to the screen. The plate
potential is determined by the setting of the delay potentiometer. If a
sufficiently strong negative trigger is supplied through V 2 to the first grid,
the fall in the cathode potential turns on the second control grid. The
establishment of plate current further reduces the potential of the first
control grid so that the second grid is turned full on. The plate can now
fall farther only as the potential of the first grid rises, by discharge of C 1
through Ri. The condenser C 1 acts as a feedback condenser, assuring
linearity of the tube response so that the plate falls linearly with the
time. When the plate reaches the potential of the second grid it no

Sec. 13-8]

GENERATION OF SHARP PULSES

501

longer falls, the feedback action ceases, and the first grid rapidly increases
in potential, pulling the cathode positive. The second grid is thus cut
off and the original condition restored. Since the plate falls at a very
linear rate to a fixed destination, the delay time is linear with the poten¬
tial from which it started its downward journey. The critical parts of the
circuit are RiC\, the delay potentiometer, and the various supply volt¬
ages. A pentode with sharp suppressor cutoff, such as the miniature
6AS6, can be substituted for the more complicated multiple-grid tube
with equally good results. The phantastron can also be used as a free-
running relaxation oscillator.

13-8. The Generation of Sharp Pulses. —Sharp pulses needed for
triggers, range markers, and other indicator uses can be generated in a
number of ways. Figure 1318 indicates three methods by which a steep

Fig. 13-18.—Simple pulse-generating circuits.

wavefront can be used for the purpose. In Fig. 1318a the advent of the
wavefront abruptly changes the potential of point A. Immediately
thereafter C starts to discharge through R, and pulses of the shape shown
result. This arrangement is usually spoken of as a “differentiating
circuit.” The steepness of the front edge of the pulse is largely deter¬
mined by that of the wavefront. In order to obtain a steep rear edge, RC
should be small, but a point is reached for a given wavefront at which
decreasing this product reduces the amplitude. The impedance of the
driving source should be small compared to R.

In Fig. 13-186, a steep wavefront sets up a shocked oscillation which is
quickly damped out by R so that essentially only one pulse is produced.
As in the case of the RC differentiator, this circuit requires a steep wave
from a low-impedance source.

If the wavefront is from a high-impedance source, or if it has insuffi¬
cient steepness or amplitude, the circuit of Fig. 1318c is useful,
particularly for positive pulses. Turning the tube on or off gives rise to a
damped oscillation as in Fig. 13T86.

A diode can be used in any of the above circuits to remove pulses of
an unwanted polarity.

502

THE RECEIVING SYSTEM-INDICATORS

[Sec. 13-8

The Blocking Oscillator .—The blocking oscillator is an inductively
coupled regenerative amplifier used in the generation of short pulses. In
the waveform diagrams of Fig. 13 T9, consider the moment t 0 . The grid
is beyond cutoff and rising exponentially toward the bias potential.
The plate is at jB + potential. . At time ti the tube begins to conduct, the
plate begins to fall, by virtue of the inductive coupling the grid is pulled
upward, and a violently regenerative action sets in which ultimately
pulls the grid far positive, drawing much current from the cathode.
Eventually, however, the rate of increase of plate current falls off and the
current to the grid pulls the latter downward. Regeneration takes place

Fiq. 13-19.—The blocking oscillator.

in the opposite direction, the grid is driven negative, and the process
repeats. The period of the oscillation is primarily determined by RC, but
the other circuit parameters do enter. Characteristics of the tube itself
enter to such an extent that the device cannot be considered as a precision
oscillator, although it can be synchronized by one of higher frequency.

The blocking oscillator can be used as a “scaling” or counting-down
circuit for a continuous pulse train of definite frequency by making the
natural period slightly longer than the expected one and applying signals
of the proper height as shown in the bottom diagram of Fig. 13-19. The
counting ratio is dependable only up to a value of 5 or 10 but synchroni¬
zation occurs to many times this value. Somewhat higher ratios can be
used by inserting a resonant circuit in the cathode.

Sec. 13 9]

ELECTRONIC SWITCHES

503

The device can be used as a “single stroke” pulse generator if the grid
is biased beyond cutoff. The circuit is then quiescent until an external
signal renders the grid conducting. The regenerative action takes place
as before, except that after it is over the grid returns to a point beyond
cutoff where it remains until a new signal is received. The circuit is often
used in this form as a means of generating sharp pulses from poorer ones,
from steep wavefronts (which are differentiated to form the triggering
impulse), from sine waves, and so on.

13-9. Electronic Switches.—An electronic switch is a device that can
change the parameters of the circuit in which it occurs. The principal
functions performed by such switches are to control the absolute potential
level of a point in the circuit, and to control the transmission or genera¬
tion of signals by switching them on and off or by choosing between
different signals. Activation of the switch can be controlled either by
the signals themselves (just as a rectifier or an overload relay is controlled)
or by a stimulus independent of the signals. In its action the switch can
be either a series element analogous to a valve that opens and closes to
block or transmit the signals, or a parallel element that, when closed,
holds a point in the circuit in a quiescent state regardless of the presence
of signals.

Clamps .—The name “clamp” is applied to a wide variety of electronic
switches which, when closed, hold or clamp two circuit points together
more or less rigidly. They differ from ordinary mechanical switches in
that their impedance is often appreciable and frequently variable, and
in that many clamps conduct current in only one direction. In fact, it is
often the latter characteristic that enables the device to function as a
switch.

The simple diode is a clamp that is closed when the anode attempts
to be positive with respect to the cathode, but open when the reverse is
true. The opening and closing may result from the waveform applied
to one of the electrodes, as in a rectifier or a detector, or one of the elec¬
trodes may be changed in potential from time to time by a separate
impulse. The use of diodes for switching purposes has been rendered more
attractive by the advent of the germanium-crystal type of rectifier, which
admirably replaces the vacuum-tube diode in many applications, par¬
ticularly those involving 50 volts or less of back emf.

The D-c Restorer .—Figure 13-20 illustrates a common method of fixing
the absolute potential taken by a point in the circuit during extreme
excursions of the signal in one direction. In the absence of the diode,
the average potential of point A must be Vo, since R furnishes the only
d-c connection. When the diode is placed in the circuit, it prevents A
from swinging more negative than Vo, so that V 0 may be thought of as a
base with respect to which the entire waveform is positive. During each

504

THE RECEIVING SYSTEM—INDICATORS

[Sec. 13-9

positive excursion of A the resistance extracts a small charge, which is
replaced by the diode on the next negative excursion. 1 The clamping
can be done at the positive extreme by reversing the diode. If fidelity of
response is of importance, the RC product must be sufficiently large to
give proper low-frequency response.

The d-c restorer has many applications, only a few of which can be
listed here. It is frequently used to insure that a grid to which unipolar

jinn

Without diode

With diode _

Fig. 13*20.—D-c restorer.

Waveform at A

■JWfbt

iliUL..,

video signals are applied is operating in the correct voltage range. This
is particularly important in the intensity modulation of a cathode-ray
tube where the tube must be just cut off for zero signal amplitude. The
d-c restorer can be used to fix the starting point of a sweep by clamping
the deflecting plate of an electrostatic tube, or the grid of a direct-coupled
sweep amplifier, between sweeps. In the above examples, the clamping
fixes the point from which signals are measured. In others, the clamping
fixes the level to which an electrode is switched “on” by a square wave,
as for example when intensifying a cathode-ray tube.

Fio. 13-21.—Diode limiters.

Biased Diodes .—Figure 13-21 illustrates two self-evident methods of
limiting the excursion of a signal by clipping off the top at a level deter¬
mined by a d-c potential difference applied to the circuit. The circuit
of Fig. 13-22, on the other hand, transmits only that portion of the signal
in which the voltage exceeds the applied potential, so that in effect the
bottom is clipped. This arrangement is of considerable importance in
time-measuring applications. If a very linear sawtooth is applied to the

1 Sometimes the resistor is made slightly more negative than To in order to hold A
tightly against the diode during the clamping period.

Sec. 13-9]

ELECTRONIC SWITCHES

505

input of the circuit, the time elapsing before an output signal appears is
proportional to the bias applied to the diode, thus providing an accurate
and easily controllable time delay (see Sec. 13-12).

Switched Clamps .—In a great many appli¬
cations the clamp must be opened and closed
over particular time intervals which may or
may not be directly related to the signals.

According to whether the clamp can conduct
in one or both directions when closed it is
classified as a one-way~(“single-sided”) or a
two-way (“double-sided”) clamp.

In the diagrams, E 0 is the potential of the
clamping point, X is the point being clamped,

A is the maximum signal amplitude, and T is the time interval over which
the clamp is to be opened. If E a is not ground potential, the voltage

Fig. 13-22.—Bottom clip-
(biased diode “ pick-off”
circuit).

per

Fig. 13*23.—One-way switched-diode clamps, (a) Switched single diodes; (6) double¬
diode clamps; (c) diode switched by cathode follower.

X is point being switched. T is length of open interval.

A is maximum amplitude of signal at X. R must be very high.

is clamping potential. Plus and minus signs are with respect to Eq.

source supplying the clamping point must be “stiff” enough to furnish
the currents drawn without appreciable potential change.

Among the simple switched clamps are the diodes of Fig. 13-23a, the

506

THE RECEIVING SYSTEM—INDICATORS

[Sec. 13-9

two diagrams indicating clamps of opposite polarities. They will, of
course, close only if the potential of point X is in the specified direction
from Eo, and even when closed they will offer no impediment to potential
changes in the opposite direction. The resistance R is included to coun¬
teract any slight leakage charges.

The requirements for the source of the switching waveform are
somewhat rigid. It must provide a satisfactory value of E 0 and a square
wave of sufficient amplitude. Furthermore, since its impedance adds to
that of the clamp, this impedance must be sufficiently low to withstand
any “pulling” by the circuit attached to X, and must be capable of dis¬
charging sufficiently rapidly any capacity associated with X.

Frequently a satisfactory square-wave source already exists in the
equipment. If not, further complexities must be added to the clamp.
Figure 13-236 shows a modification that can be used when the source has a

Fig. 13-24.—One-way triode clamps, (a) Positive clamp; (b) negative clamp.

sufficiently low impedance but an improper d-c level. The tube Fi
serves the same function as before and F 2 acts as a d-c restorer. The
presence of the resistor R i increases the requirement for a low-impedance
source.

If the waveform source has high impedance, it is necessary to intro¬
duce a cathode follower as shown in Fig. 13 23c. The clamping takes
place through the diode and Re, thus R i must not be too large. This in
turn requires considerable current through V 2 during the clamping inter¬
val. The proper d-c level for the switching signal can usually be chosen
by a proper choice of R 2 , R 3 , and the bias potential. If not, it may be
necessary to use condenser coupling and a d-c restorer on the cathode-
follower grid. The corresponding negative clamp is not used, since the
circuit of Fig. 13-246 accomplishes the same results more simply.

Figure 13-24 illustrates one-way clamps using a single triode. 1 In
both cases the clamping is done through the tube impedance as viewed
from X. In the positive clamp this impedance is unfortunately rather
large so that this clamp is not very “tight.” The negative one, on the

1 The well-known Rossi coincidence circuit is an example of a triode clamp.

Sec. 13-9]

ELECTRONIC SWITCHES

507

other hand, is satisfactory in this respect. Care must be taken in the
latter that “droop” in the switching-off pulse does not allow the grid to
go too far positive when the clamp is closed, for this can produce over¬
shoot through grid-cathode diode action. Square-wave droop can also
cause overshoot in the positive clamp if the clamping is not tight.

The relative merits of the various single-sided clamps depend upon
the uses to which they are to be put, the type of switching source avail¬
able, and so on. If a proper driving source already exists, the simple
diode (Fig. 13 23a) is cheapest and best. If not, the triode of Fig. 13-246
best combines simplicity and good characteristics among the negative

(“) ( 6 )

Fig. 13-25.—Two-way clamps, (a) Two-way double-triode clamp; (b) two-way four-diode

clamp.

clamps, and Fig. 13-23c is the best and Fig. 13-24a is the simplest of the
positive clamps. If the load impedance is high, the latter may be quite
satisfactory.

Two-way clamps are usually made up of two one-way units of opposite
polarities, as indicated in Fig. 13-25a and 6. The requirements and
shortcomings of the corresponding one-way clamps apply equally here.
The “phase splitter” of Fig. 13-12 provides an excellent driving circuit
for Fig. 13-256 if it is necessary to provide a special one. If a proper
driving source is used, the four-diode clamp can be much “tighter” than
the two triodes in the positive direction. Furthermore, the capacity
coupling through the two triodes adds, whereas in the diode circuit the
effects of the opposite waves tend to cancel. On the other hand, the
double-triode circuit is much the cheaper, particularly if a special driving
circuit must be provided for the diodes.

508

THE RECEIVING SYSTEM—INDICATOR

[Sec. 13-9

In certain applications where the clamp is used as a series element,
it is essential that the current drawn from the reference point be as small
as possible. Even such small currents as those drawn by the grid cir¬
cuits of Fig. 13-25a may be objectionable. In the circuit of Fig. 13-26,
the transformer-coupled grid circuits form closed loops which draw no
current whatever from the reference point.

This circuit is widely used as a demodulator in cases where the phase
of the carrier with respect to the reference signal is of importance. The
waveform to be demodulated is applied to the input terminal of the cir¬
cuit and the transformer is excited by an unmodulated wave which is
exactly in or exactly out of phase with the carrier. Because of grid
current, the two tubes will bias themselves to such a point that they are

turned on only at the peak of the keying wave¬
form; hence the device is a peak detector.
The polarity of the rectified signal at the out¬
put terminal will depend upon which of the two
phase relationships exists. This property is
useful in such applications as the demodula¬
tion of a carrier wave modulated by a synchro.
As pointed out in Sec. 13-4, the output signal
at a given phase of the input signal has oppo-

Fio. 13-26.— Two-way site polarity on either side of a null position of
double-triode clamp with S y nc jj ro ro tor; in other words, the carrier

tranaformer-couplea switching. ,

undergoes a 180 phase change as the synchro
passes through a null. Thus, when the circuit of Fig. 13-26 is used as a
demodulator, the output voltage is positive or negative depending upon
whether the synchro rotor is oriented positively or negatively with respect
to the null position.

The switching signal always “leaks” through the clamp tube to some
extent by capacity coupling, particularly at the “off-point.” For this
reason the switching signal should be no steeper or larger than necessary.
Because of this, pentodes are sometimes used in such circuits as those of
Fig. 13-24o and 13-25a. This increases the impedance of the positive
clamp, but is only necessary when the load impedance is also high.

Gated Amplifiers .—-An important form of electronic switch of the
nonclamping variety is a “gated” amplifier tube, in which the switching
signal is applied to an electrode in such a way that the electron current to
the plate is interrupted and no signal can pass. Figure 13-27 illustrates
various methods which are more or less self-explanatory. 1 All of these
are widely used as pulse coincidence circuits 2 or to select the pulse or

1 It is possible to combine two or more of these methods so that three or more
electrodes have signals.

’In the case of pulse coincidence there is, of course, no distinction as to which
electrode is being switched.

Sec. 13-91

ELECTRONIC SWITCHES

509

pulses occurring during a given time interval. The triode can be used
only if both signals are limited, since otherwise it could be turned on by

Fig. 13-27.—Gated amplifiers, (a) Switched triode; (b) multicontrol tube switched on
second control grid; (c) suppressor switching; (d) screen switching.

one alone. The circuits of diagrams (6) and (c) of Fig. 13-27 require the
least power input. The 6AS6, which has a sharp suppressor cutoff, is
the most satisfactory tube unless considerable load current is needed.
Since none of the tubes that can
deliver large currents has either a
second control electrode or a sharp
suppressor cutoff, it is customary to
use screen gating when the current
requirements are high. In the case of
video signals, the tube must have a
very sharp cutoff on the signal grid;
even then it is usually necessary to
choose between an extreme bias, which
sacrifices gain at low signal ampli¬
tudes, and a lesser one, which allows a
“plateau” to be transmitted. The use of two tubes in the way described
in the next paragraph is more satisfactory.

Two such switches can be used in parallel to alternate signals from
two sources, as shown in Fig. 13-28. In this case the simultaneous but
opposite switching of the two tubes eliminates the plateau if the two cir-

Fig. 13-28. —Switching of alternate
signals.

510

THE RECEIVING SYSTEM—INDICATORS

[Sec. 1310

cuits are properly matched, and the signal grids can therefore be in full
operation at all times. Since it is essential that the proper d-c levels be
maintained when the signal duty interval is large, d-c restorers must
follow any a-c coupling. This circuit is often used as a single-channel
switch, the signals being applied to one tube, and the other serving merely
to cancel the plateau. The circuit may also be adapted to suppressor
grid switching.

13-10. Sawtooth Generators. —The sawtooth waveforms used as a
basis for range sweeps and in certain varieties of precision timing circuits
are practically always generated by a wave-forming network that is
switched on and off by some sort of clamp.

The basic action of all such devices can be illustrated by the simple
circuit of Fig. 13-29. When S, a single clamp of proper polarity, is closed,
an equilibrium state is reached in which X differs from ground potential

Fig. 13-29.—Basic sawtooth generator.

only by the small drop across R g . If S is suddenly opened, the current
is shifted from S to C, and the latter starts to charge exponentially at a
rate determined by R, C, and E. The rising wave of the sawtooth is an
exponential of time constant RC, as indicated in Waveform 2 of Fig.
13-29. If the sawtooth has an amplitude small compared to E —that is,
if RC » T— the rise is approximately linear (Waveform 3). Such saw¬
tooth generators are widely used in cases where no great precision is
required.

When various sweep speeds are to be used, it is necessary to change
the rate of rise of the sawtooth. This can be done in discrete fashion by
switching the condenser, the resistance, or, within limits, the charging
voltage. Continuous variation is most satisfactorily accomplished by
using a rheostat for R (unless the control is remote) or by varying E
through a potentiometer.

Figure 13-30 illustrates both positive and negative saw-tooth genera¬
tors using single-triode clamps. If waves of both polarities are desired,
the two circuits of this figure can be combined, or a single tube can be

Sec. 13 10]

SAWTOOTH GENERATORS

511

used to perform both functions in a somewhat less satisfactory manner.
More often, however, a single wave is generated and the second obtained
from it by a phase-inverting amplifier.

More sophisticated sawtooth generators are necessary when precision
is required. All of these endeavor to provide great linearity in one of the

Fig. 13-30.—Sawtooth generators using triode clamps.

following ways: (1) by substituting a “constant current” device for R ;
(2) by adding the condenser voltage to E, thereby keeping the current
through R constant; (3) by including a high-gain negative-feedback
amplifier, so that only an extremely small voltage need be developed
across the condenser.

1. A pentode can be used as a constant-current device. This method

has been little used in radar, however, partly because of general
complications and partly be- + + +

cause when a pentode is used t 1 _ ‘ I

in a positive sawtooth gener- S fii f —N >

ator it is necessary to provide > ' ’ 1 ! 1 '

a floating screen-voltage
supply.

2. Figure 13-31 illustrates the
use of a cathode follower to
keep the voltage drop across
R nearly constant. That U~
part above the switch indi¬
cates three alternatives.

Neglecting the a-c drop
across C i, the positive feed-
back raises point Y by an Switch indicates alternate methods,
amount E X G, where G is the

gain of the cathode follower and E x the potential of the point X.
Thus the drop across R is given by

E — E x + EJJ = E — E x { 1 - G)

«R i and K-.

512

THE RECEIVING SYSTEM—INDICATORS

[Sec. 1310

as compared to E — E x were the feedback not present; the effect
of the amplifier is the same as that of using a supply voltage
E/( 1 — G). For a triode, 1/(1 — G) may be as much as 20, and
for a pentode as much as 200.

Use of the resistor R i is simplest, but it has important disadvan¬
tages. The charge leaking off C i through R and R i must be returned
through them during recycling, and since the time constant of the
circuit must be large compared to T this requires appreciable time.
If the duty ratio is appreciable, a d-c shift results which depends
on that ratio. This circuit can, therefore, be used only when the

Fig. 13-32.—Sawtooth generators incorporating negative feedback.

ratio is very small or very constant. Furthermore, the presence
of R i reduces the feedback gain. The diode avoids these diffi¬
culties, since it cuts off during the duty interval but closes to give a
low impedance during recycling. The triode cuts off almost as
quickly as the diode and provides a convenient method of provid¬
ing voltage control since it draws no current from the variable
potential source.

When extreme precision is required, the defects due to the charge
drawn from C i and the less-than-unity gain of the cathode follower
may be important. These errors can be completely eliminated by
use of a more complicated amplifier of gain greater than 1, the
excess gain compensating for the drop across C i. An alternative
is to add to the sawtooth a compensating voltage which, should
be approximately proportional to the integral of the sawtooth.

Sec. 13-10]

SAWTOOTH GENERATORS

513

This method is used in the precision delay circuit of Fig. 13-36,
described in the next section.

3. The most common method of using linear amplifier gain to keep
the necessary signal voltage small is illustrated in the diagrams of
Fig. 13-32. The amplified signal is applied to the “bottom” of the
condenser, so that the potential of X changes only by the difference
between the charge across the condenser and that fed back. Thus
the change in potential across R is kept very small and the charging
current is very constant. The most commonly used of such
methods is the Miller “run-down” circuit of Fig. 13-326 and c.
The two circuits shown differ only in the methods of switching.
In both cases the amplifier consists of a single tube on whose grid
the original signal is formed. The entire plate swing is applied
to the condenser, so that the feedback ratio is 1. In the case of
suppressor switching, all of the current goes to the screen between
sweeps. The control grid is held against the cathode by virtue
of its positive bias. When the suppressor is switched on, most of
the current transfers to the plate, which experiences a negative
surge that is passed on to the control grid. The sawtooth genera¬
tion then begins as indicated in the waveform diagrams. The step
at the beginning of the sawtooth is in some cases detrimental and
in others useful.

INDICES

It is always desirable and usually mandatory to provide some form
of quantitative indices or markers for the radar indicator. These may
consist simply of a grid work of lines or, when high accuracy is required,
of one or more movable indices. In addition, it is often desirable to
superpose some form of map or chart on a radar display, in order to pro¬
vide accurate correlation with fixed echoes for navigational purposes or
to show at a glance the geographical position of a ship or aircraft target.
Markers can be provided either by placing a surface containing the marks
as nearly as possible in optical superposition with the display, or by
modulating the electron beam in such a way that the marks appear as
part of the display itself.

Indices or charts ruled on a transparency over the tube face are the
simplest of all to provide, but their use results in errors due to display
inaccuracies, to parallax, and to faulty interpolation. Furthermore, if
the origin of the display is to be moved, it is necessary to provide a
corresponding motion of the reference system, which is usually cumber¬
some, or if only a few positions are involved, to furnish multiple sets of
marks in such a way that no confusion results. The methods of optical
superposition described in Sec. 7-3 largely eliminate parallax and are

514

THE RECEIVING SYSTEM—INDICATORS

[Sec. 13-11

helpful in the case of multiple indices, but their principal usefulness is in
connection with plotting and the use of charts.

“Electronic” marks eliminate or reduce many of these difficulties.
Parallax errors are entirely eliminated. Since the indices are generated
by precision methods that are independent of the formation of the
display geometry, they automatically fall in their proper place on the
display regardless of where it may be centered or how much it may be
deformed or distorted. In general, electronic methods of producing
interpolation indices are far less cumbersome than mechanical ones.
However, in the case of a slow scan the intermittent nature of the display
makes it difficult to set an index on the echo, unless rather complicated
switching methods are introduced to provide the indices at more frequent
intervals.

Electronic indices are invariably used for range determinations, since
they can be readily provided with a high degree of precision and since the
radar data are inherently capable of providing great accuracy in range.
In cases where the fundamental data are not so precise, the choice depends
upon circumstances. Electronic marks are always used if the display
is to be continuously movable in position or in size, but in many of the
cases where only a few discrete changes are involved, external markers
are sufficiently simpler to warrant their use.

The following two sections will describe methods of providing directly
viewed electronic indices; auxiliary optical aids have already been
described in Chap. 7.

13-11. Angle Indices. —Because of their simplicity, fixed angle
indices ruled on a transparency are widely used in spite of the inaccura¬
cies described above. The inherent data are usually far less accurate
than those of range. Furthermore, in many applications, such as that
of homing, the angle of interest changes slowly if at all and there is time
for repeated observations. Parallax errors are made as small as possible
by placing the scale very close to the tube face, and in many cases by
ruling on both sides of a rather thick transparency in order to provide a
line of sight.

Movable angle indices of the same type are little used except in the
important case of the centered PPI, where the motion is one of simple
rotation. The index or “cursor” may consist of a thin metal strip
viewed edgewise or of a transparency with a ruled line or a thin slit
milled through it. It is supported by a ring bearing larger than the tube
face and is usually turned by means of a hand crank to which a data
transmitter may be attached if desired. Readings are made from a
circular scale at the edge of the tube.

Fixed Electronic Angle Indices .—An electronic angle index can be
provided by brightening the cathode-rav tube for a few sweeps so that a

Sec. 1311]

ANGLE INDICES

515

bright narrow line is produced at a given azimuth. The electrical
impulse necessary to do this can be provided in any of several ways.

1. The simplest method involves the use of mechanical contactors
on the scanner or on any mechanical repeater of the scanner
motion. The contact is usually made by a microswitch operated
by a cam on a rotating shaft. Since it is impossible to open and
close the switch in a short enough angular interval, unless the scan
is very slow, some device for producing a short pulse must be
introduced. This can consist of a flip-flop triggered by the micro-
switch although, for medium or slow 7 scans, it is possible to make
use of the transit time of a mechanical relay. 1 In order to produce
a set of markers, an equal number of cams on a one-speed shaft or

few r e'r cams on a higher-speed shaft can be used. The latter
method is preferable because of the cleaner action,

2. Figure 13-33 illustrates a method for generating angle marks by
using a photocell mounted behind a slotted rotating disk. Since
the slots can be made extremely narrow 7 and no inertia is involved,
this method produces extremely clean-cut markers. The disk
can turn at the scanner speed and have as many slots as there are
markers, or it can be geared up and have fewer slots.

3. A method of using a carrier modulated by a synchro is illustrated
in Fig. 13-34. (The figure actually illustrates a movable index.
In the case of fixed indices, the signals can be taken from the first
synchro and the second one omitted.) The modulation introduced
by the rotating synchro is sinusoidal with scanner rotation; if the
latter is uniform the modulation envelope obtained from the
detector has this waveform. The sharp cusp occurring at the nulls

1 See, for example, Fig. 4-2 of Vol. 22.

516

THE RECEIVING SYSTEM—INDICATORS

[Sec. 1311

is the desired signal. Since there are two nulls per revolution, the
synchro must be geared up by>.a ratio equal to half the number of
markers. In the figure the null is used as a switching signal for an
oscillator of frequency approximately one megacycle per second.
The train of pulses is “rectified” by the cathode-ray tube, so that

the marker appears as a row of dots which merge except on fairly
fast sweeps. An oscillation of this sort is preferable to a simple
rectangular pulse if the signals are to be passed through mixing
or other circuits whose low-frequency response is not as good as
demanded by the very long (as much as tq sec) marker pulse.

Movable Electronic Angle Indices .—The methods of producing fixed
electronic angle indices can be extended to provide movable ones. This
can most easily be done, with the synchro method of Fig. 13 34, by using

Sec. 13111

ANGLE INDICES

517

the second synchro to introduce the differential setting. The two nulls
will result in two signal markers 180° apart. If this is undesirable one
of them can be removed by a method involving the use of a multiphase
rotor in the second synchro. A second modulation envelope, 90° out of
phase with the first, is obtained and used to blank one of the markers
(see Fig. 4-5, Vol. 22).

The production of a movable index by the contactor or photocell
method requires that the differential setting be made mechanically.
This method is seldom used unless the indicator contains a mechanical
repetition of the scanner motion.

Movable electronic indices appear on the indicator only when the
cathode-ray beam is on a particular part of the tube face. To set an
index on an echo, it is essential to be able to observe the results of moving
the index. If the scan is rapid, the operator has frequent chances to do
so, but if it is slow he cannot cor¬
rect an error for several seconds.

This is not too serious in the case
of the movable range marker,
because it appears at all azimuths
and can be “ steered ” in the proper
direction as it approaches the per¬
sistent echo remaining from the
previous scan.

An angle index, on the other
hand, if formed by the methods of
the preceding paragraph will “flash up” only as the scanner passes by.
The operator has no chance to make a correction before the next scan, and
even then the correction must be an educated guess. It is very difficult
to make accurate settings within the space of a few scans, especially if
there is relative motion between radar set and target. 1

It is, therefore, essential on slow scans to use some other method. For
all displays except rotating-coil PPI’s, the so-called “substitution”
method illustrated in Fig. 13-35 can be used. From time to time control
of the display is switched from the regular angle data transmitter to one
that can be set by the operator. During these intervals the direction
taken by the range sweep is determined by the setting of the “substitu¬
tion” transmitter and is thus under the control of the operator. The
switching may be made to occur automatically on a certain fraction of the
range sweep cycles equally distributed throughout the scan (which
requires rapid electronic switching), or it may occur continuously over an

1 The problem is greatly simplified if aided tracking is used—that is, if some sort of
computer moves the index in accordance with the relative motion, using knowledge
acquired by making the best settings possible in the past.

Fig. 13-35.—Substitution method for movable
angle index.

518

THE RECEIVING SYSTEM—INDICATORS

[Sec. 1312

appreciable sector of the scan remote from the one of interest, in which
case the switching can be slower and in some cases mechanical. In the
first case the index appears continuously, and in the second it appears
during an appreciable fraction of the scan. In either event, the operator
is able to make this setting w T hile the index is present. The method is not
applicable to a rotating-coil system because of its inertia. Fortunately,
however, this type of display is itself exceedingly accurate in angle, so
that the mechanical cursor can be used on the centered PPI display with
little error except that due to parallax.

13*12. Range and Height Indices; Synchronization. —Since the
providing of electronic range indices is frequently intimately associated
wdth synchronization, these topics can best be discussed together. The
discussion will be simplified if movable indices are described first.

Methods of Obtaining Movable Markers .—In general, four methods are
used for obtaining a continuously movable marker. In increasing order
of the precision that can be obtained they are: ( 1 ) the cathode-coupled
multivibrator; (2) the phantastron; (3) a timing circuit based on a linear
sawtooth; (4) the phase-shifting of a precision sinusoid.

The use of the multivibrator or the phantastron for time-delay pur¬
poses has been discussed in the sections describing those devices and no
further description need be given.

The use of a sawtooth voltage wave for timing depends upon the fact
that the time taken for such a wave to reach a given voltage is propor¬
tional to the voltage chosen. Figure 13 36 illustrates a circuit by means
of which this principle can be very precisely applied. Tubes Fi, F 5 , Fj,
and F 4 constitute a precision sawtooth generator. The drop across the
condenser C and the lack of unity gain in the cathode follower (Sec.
13-10) are compensated by the network composed of C ' 2 and /f 2 w'hich
integrates the sawtooth appearing on the cathode of V 3 and thus provides
across C 2 a correction proportional to t 2 . The sav r tooth waveform is
applied to the plate of diode F 5 , whose cathode has a positive bias of an
amount determined by the setting of the delay potentiometer. Because
of this bias, no signal passes through the diode until the sawtooth has
reached a definite amplitude, determined by the bias value. When the
critical amplitude is reached (at time ti on the waveform diagram), the
remainder of the sawtooth appears on the grid of IT. This partial
sawtooth is amplified by F 6 , differentiated in the plate-loading trans¬
former, further amplified in F 7 , and ultimately used to trigger.the single¬
stroke blocking oscillator circuit of F 8 , vdiich produces the delayed pulse.
The slope control determines the range scale and the zero-set resistors
balance out the combined effects of the starting time of the switching
square wave, the starting voltage of the sawtooth, and the conduction
point of the diode. The critical circuit elements in addition to those in

Sec. 1312] RANGE AND HEIGHT INDICES ; SYNCHRONIZATION 519

520

THE RECEIVING SYSTEM—INDICATORS

[Sec. 13-12

the sawtooth generator are the delay potentiometer and its associated
resistors and the diode F 6 . The circuit is described in detail in Chaps.
5 and 6 of Vol. 20 and Chap. 13 of Vol. 19.

The most accurate timing device at present available is a precision
oscillator. This device can be used for the generation of a movable
marker only by some method involving a continuous shifting of its phase.
Extremely precise indices can be generated in this way, although the
error of most phase-shifting elements is large (0.3 per cent). Space
permits no description of this method but the reader is referred to Chap.
4 of Vol. 20 of this series.

Movable Height Marker .—The indices used for determining height on
the RHI or the type E display are usually engraved mechanical ones.
Often, however, a movable electronic index is provided. Neglecting the
earth’s curvature, the time t at which an index of constant height h should
appear on an individual sweep is defined by the equation

c 2 h

h = R sin 0 = . t sin </> or t = —t —->

2 c sin 0

where R is slant range, 4> is elevation angle, and c the velocity of light.
The timing can most easily be done by means of a linear-sawtooth delay
circuit. A voltage proportional to sin <p is used as the supply potential
for the sawtooth generator. Thus, for a given diode bias, the slope of
the sawtooth is proportional to sin <t> and the time delay is proportional
to 1/sin <t>. The height represented can then be linearly controlled by
varying the diode bias. In general, the inherent radar data are not
accurate enough to justify circuits as precise as that of Fig. 13-36. At
large ranges a correction must be made for the earth’s curvature. This
can be done with sufficient accuracy by adding a t 2 term to the sawtooth
voltage, such a term being obtainable by integrating the sawtooth itself
as in Fig. 13-36.

Discrete Timing Markers .—Discrete indices are invariably produced
by deriving sharp pulses from a sinusoid that is properly phased with
respect to the modulator pulse. The exact methods depend upon cir¬
cumstances and in particular upon whether or not the marker circuit
provides the synchronization. Figure 13-37 gives a typical example in
which it does so; Fig. 13-38, one in which it does not.

The oscillator of Fig. 13-37 can be of any type satisfying the particular
precision requirements. The original sinusoid is amplified and clipped
to produce a symmetrical square wave of the same frequency. The
“negative-going” edge of this square wave is then used to trigger a
single-stroke blocking oscillator. The frequency of the sinusoidal oscil¬
lator, and therefore of the pulses, is made equal to that of the most closely

Sec. 1312] RANGE AND HEIGHT INDICES ; SYNCHRONIZATION 521

spaced markers desired. 1 Lower-frequency markers are provided by
scaling circuits. A final scaling circuit provides pulses of proper frequency
for triggering the modulator, the sweeps, etc. In the figure it is assumed
that the desired frequency values are successively integral multiples of
the lowest frequency. If this is not the case, multiple counting channels
are necessary; for simplicity an integral relationship is usually chosen.

When synchronization is external, the oscillator must be shock-
excited. Figure 13 38 illustrates an /X'-oscillator widely used in medium-
precision applications. When Vi is conducting, the circuit is quiescent
and energy is stored in the inductance by virtue of the cathode current.

sinusoid VVVXAAAAAAAAAAAtV
f>. square wave _jn_jnjn_xijnjnjnjnjnjn_njn_n_ri_n_ri_j

c. 1 mile marks I I I I I I I I I I I I I I I _

(compressed scale) llllllllllllllllllll lllll-—11111111

d. 5 mile marks -1-1 I 1 I I I 1 I 1 I I I I I I I I I I I I I 1 I I I I I I I I I I

e. 20-mile marks I _|_|_|_|_|_ I I _

f. Trigger _ I_J_

Fig. 13-37.—Derivation of pulses from c-w oscillator.

Interruption of this current by the square wave shock-excites the oscillat¬
ing circuit. The resulting voltage wave has an initial phase of zero
and an approximate amplitude of / -\/2 L/C. The constants of the
Hartley circuit of V 2 are so chosen that this initial amplitude is just
preserved. In the present example the amplification necessary to pro¬
duce steep wave fronts is provided by the regenerative amplifier formed
by V 3 , V 4 . Each time that V 4 is turned on, the surge of current through
its plate circuit 2 triggers the single-stroke blocking oscillator formed by
Vi, giving rise to the desired pulse. It should be noted that a slight
delay is inherent in the production of the first pulse, since a short but
finite time is required to turn on F 4 . Later pulses are all displaced by

1 For example, in the case of 1-mile markers this frequency is 93.12 kc/sec.

2 The current necessary to charge C 3 increases the positiveness of this action.

522

THE RECEIVING SYSTEM—INDICATORS

[Sec. 1312

the same amount. Since no pulse is involved in the reverse regeneration,
the exact phase at which it appears is immaterial. The precision of the
circuit is largely determined by L and C, which should be temperature-
compensated and well shielded. Since R 1 has some effect on frequency,
it should be of a reasonably stable type. Frequency adjustment is best
made by slug-tuning the coil L. Once aligned, a well-designed unit
should maintain its calibration to better than 1 per cent.

Many variations of this circuit, mostly simplifications, have been
used. For example, if only a few markers are required on each pulse
cycle, Vi can be omitted, since the high-Q coils in the oscillating circuit

will ring with sufficient amplitude for several cycles. In many cases a
simpler pulse generator can be used.

When two or more marker frequencies are needed alternatively, the
resonant circuit is switched. Scaling-down is rarely used, since more
vacuum tubes would be involved and since it would be necessary to
recycle the counting circuits on each pulse cycle.

Delayed Sweeps .—Any of the timing circuits just discussed can be
used to provide the trigger for a delayed, expanded sweep, and in fact
this function can be combined with that of accurate range determination.
The most usual method using continuous delays is illustrated in the block
diagram of Fig. 13-39. The precision variable-delay circuit directly
provides the trigger for the delayed sweep. An index marker is pro¬
vided at the center of the sweep by a second fixed-delay circuit, usually
a flip-fl«p, whose action is initiated by the sweep trigger. The timing
arrangements are obvious from the waveform diagram. The total range

Sec. 13 121 RANGE AND HEIGHT INDICES ; SYNCHRONIZATION 523

Trigger

Precision

variable

delay

r 1

Fixed

delay

Marker

pulse

Delayed sweep trigger

Trigger

Delayed trigger

to the center of the sweep corresponds to the sum of the two delays, but
the fixed delay can be included in the calibration.

Range determinations made in
this way require that the display
pattern be moved as coincidence
between the echo and the marker
is established. If this is undesira¬
ble, the marker-pulse delay can also
be made variable and the two
added, either by the operator or by
an arrangement for mechanically
summing the settings of the two
control knobs. This method is
more convenient than separating
the delay and the measuring cir¬
cuits, since it ensures that the marker will always appear on the sweep
regardless of the setting of the two knobs.

A discrete set of pulses is frequently used to provide a stepwise sweep
delay. The usual method is illustrated in Fig. 13-40. The principal

Timing pulse

Delayed sweep
Marker pulse

Fio.

13-39.—Synchronization of delayed
sweep with precision range index.

Modulator

Coarse

Rectangular

Coincidence

Dulse

delay

Pulse- I
selecting
gate

circuit

Stepwise 1

selecting

pulse

control

r TJlUL.- 1 Inter-

-•1 Interpolating r--

' delay J polating
- J marker

—► Delayed-sweep
trigger

Modulator pulse
Timing pulse
Interval selecting pulse .
Pulse-selecting gate

i i i i i

i i i i

Delayed-sweep trigger

Delayed sweep

Interpolation marker_ I _I_

Fig. 13-40.—Discrete sweep delay.

problem is that of selecting the proper pulse. This is done by coincidence
between the pulse and a gate initiated by a delay circuit sufficiently
accurate to ensure that the gate brackets the proper pulse (see waveform
diagrams). The length of the delayed sweep is usually made twice that
of the delay steps, in order to ensure sufficient overlap. If desired, the
delayed trigger may also be used to initiate an interpolating range circuit

524

THE RECEIVING SYSTEM—INDICATORS

[Sec. 1313

as illustrated by the dotted part of Fig. 13-40. It is quite feasible to
provide discrete indices on the expanded sweep by providing pulses of
sufficiently high frequency to be useful. These may, for example, arise
from an earlier stage of the chain of Fig. 13-37 than that which provides
the delaying trigger pulses. Such multiple-scale systems are described
in Chap. 6 of Vol. 20 of the series.

DISPLAY SYNTHESIS

Displays are synthesized by combining the components and tech¬
niques described in the preceding sections of this chapter. Although space
will permit only brief descriptions of some of the more important and
jharacteristic of the methods used, variations to fit particular circum¬
stances and extensions to other applications will be apparent in many
cases.

13-13. The Design of A-scopes. —This section will describe two
methods for synthesizing type A displays, one of extreme simplicity
intended only for test and monitoring purposes, and the other of a more
elegant form.

A Simple A-scope .—In Fig. 13-41 simplicity of design has been carried
to the extreme in producing an indicator intended only for testing or
monitoring applications in which brightness and sweep linearity are not
of great importance. The operation of the circuits is as follows. Tube
V la and the first three elements of V 2 form a flip-flop providing a square
wave, A, for intensifying the cathode-ray tube and at the same time
cutting off the current from the plate of V 2 , on which a positive saw-tooth
is formed by the usual condenser charging circuit. One of the horizontal
deflecting plates of the CRT is driven directly by this saw-tooth; the other,
by a negative sawtooth provided by the inverting amplifier Vv>, which
is provided with cathode feedback. Since a rather large saw-tooth
( = 100 volts) is generated without exponential correction, the sweep
slows down slightly toward the end.

As is shown, two sweep speeds are provided, one of 300 Msec using C 2
as the integrating condenser, and a second of approximately 5 gsec using
the stray capacity at point B. More values can of course be provided
by adding more switch points and condensers. In the interest of sim¬
plicity the flip-flop is not switched, being left on for the duration of the
slower sweep. When the faster sweep is used, the beam is swept entirely
off the tube face and remains off until termination of the flip-flop.

The video amplifier illustrated has a bandwidth of about 1 Mc/sec,
the exact value depending upon the stray capacity introduced by the
connecting circuits.

The power supply should include a conventional rectifier and /.C-filter
to provide the 300 volts direct current and an /fC-filtered negative supply

DESIGN OF A-SCOPES

Sweep generator

Inverter

-INDICATORS

Sec. 1313]

DESIGN OF A-SCOPES

527

from the same transformer. Since the load on the latter is extremely
small, the voltage will correspond to nearly the peak amplitude of the
transformer output wave.

The circuit can readily be adapted to larger cathode-ray tubes. For
the 3BP1 (3 in.) it is only necessary to alter the sawtooth-generator
charging resistor to compensate for a slightly different deflection sensi¬
tivity. A much more intense display can be provided by using the split-
accelerator type 3JP1. In this case approximately —800 volts should be
applied to the cathode and 1000 volts to the third anode. The second
grid and the focus electrode are kept at suitable intermediate voltages.
Auxiliary facilities, such as range-measuring circuits or sweep delays, can
be added, but when these are desired it is usually preferable to use a more
elegant basic indicator.

A General-purpose A-scape .—'The block diagram of Fig. 13-42 illus¬
trates an A-scope having provisions for both delayed and undelayed
sweeps, fixed range markers, and an interpolating range marker. The
cathode-ray tube used is of the post-deflection-acceleration type using up
to 4000 volts over-all with reasonable deflection sensitivity (Sec. 13.1).

A precision variable delay and a fixed delay are combined to furnish a
delayed trigger and a precision range marker as described in connection
with Fig. 13-39. The marker can be used to determine the desired delay
in advance by setting it at the point of interest. Since the minimum
range of the marker is increased by the fixed delay, a switch (S 2 ) is pro¬
vided for substituting the earlier pulse when an undelayed sweep is being
used at short ranges. The dial calibration must then be changed accord¬
ingly, the simplest method being the use of a second scale.

The sweep circuits, which comprise the top row of the block diagram,
are shown schematically below. On being triggered, the square-wave
generator V 2 brightens the cathode-ray tube, switches the sawtooth
generator, and, when the sweep is not delayed, also switches the fixed-
marker generator. The sawtooth generator V 3 , Vi (see Sec. 1310)
furnishes a very linear positive sawtooth which is of sufficient amplitude
to drive one of the horizontal deflecting plates of the cathode-ray tube.
The inverting amplifier V 3a , which drives the opposite CRT plate, is
made very linear by plate-to-grid feedback. The equal condensers
in the grid circuit ensure that the gain from point B to point C is unity,
to keep the mean potential of the deflecting plates constant (Sec. 13 1).
The d-c restorers V 6 hold the sweep origin fixed regardless of duty ratio.

Two fixed and one variable sweep speeds are shown. The square-
wave generator is automatically turned off at the proper time by the
action of V i. The positive sawtooth is delivered to the grid of V ,, which
is biased beyond cutoff by such an amount that it starts to amplify just
as the sawtooth reaches the desired peak amplitude. The signal on the

528

THE RECEIVING SYSTEM—INDICATORS

[Sec. i3-14

plate of V i triggers off the flopover. This method is extremely useful
when a variable sweep is involved, since it avoids the necessity of “track¬
ing” two potentiometers.

13-14. B-scope Design. —The essentials for providing a type B display
have been shown in Fig. 12T and described in Sec. 12-2. Either an
electrostatic or a magnetic cathode-ray tube can be used, the former
being much cheaper but far less satisfactory. Except for the final
amplifiers the circuit requirements in a given situation are similar, no
matter which tube type is used.

An electrostatic B-scope can be built around the range sweep circuits
of the A-scope of Fig. 13-42, 1 the only changes necessary being to move
the video and marker signals to the intensity-modulating elements of the
CRT and to provide the azimuth sweeps. A potentiometer is almost
invariably used as the azimuth data transmitter for an electrostatic
tube. It may drive the deflecting plates directly, in which case it must
have two brushes delivering peak potentials of from one to two hundred
volts. Alternatively, a push-pull direct-coupled amplifier is inserted.
If the potentiometer has only one brush, phase inversion is accomplished
by common cathode-coupling like that used in amplifier V t , F 6 of Fig.
13-435.

Magnetic B-scopes .—Magnetic B-scopes of varying degrees of com¬
plexity have been used. If the center of the display is to remain fixed
in angle, a potentiometer is usually employed and the only essential
departure from A-scope design is in the amplifiers. In many applica¬
tions, however, more flexibility is desired, requiring more complicated
methods. Figure 13-43 illustrates an example in which both the center
of the sector and the scale factor in each direction can be chosen at will.

In each diagram the top row comprises the azimuth sweep circuits.
An audio oscillator Vi excites the first of a pair of- differentially connected
synchros by using its rotor in an oscillating circuit. The excited synchro
is rotated in synchronism with the scanner, the second being manually
oriented to select the desired sector (Sec. 13-4). As many as five or six
B-scopes with independent sector selection can be operated in this way
from a single oscillator and antenna synchro. The modulated signal
from the second synchro is passed through an impedance-changing
cathode follower Vi, demodulated by a phase-sensitive rectifier Vs (Sec.
13-9), then smoothed by an AC-filter. The azimuth deflecting circuit is
completed by the push-pull amplifier Vi, IT, in which the latter tube
receives its exciting signal by virtue of the common cathode and screen
resistors.

If continuous rotation is used, rather than sector scanning, the sweep

1 The circuit of Fig. 13-41 is not suited for a cathode-ray tube using accelerating
potentials as high as those required for a B-scope with a persistent screen.

Coil currents ..

M 2

Azimuth circuits

wm— m

sector

Range sweep circuits

r _,

i—i

i_r

i_i

Fk;. 13-43a.—Magnetic B-scope, schematic diagram.

Small vertical arrows on waveforms at left indicate the timing of the transmitter trigger.

Sec. 13 14] B-SCOPE DESIGN 529

530 THE RECEIVING SYSTEM—INDICATORS [Sec. 1314

Sec. 1314]

B-SCOPE DESIGN

531

will pass back across the tube when the scanner is pointing 180° away
from the sector being viewed; it is thus necessary to blank the tube during
that interval. This is accomplished by the circuit of Vi a , V lb , V s , and V s .
By means of a resistance network across two phases of the differential
synchro a voltage 1 is obtained which has a modulation phase 90° removed
from that of the azimuthal sweep voltage. After rectification by V 9 ,
this signal controls the action of the flopover V 8 . The latter triggers in
opposite directions at two points which are symmetrical in scan angle
with respect to the center of the sector displayed. The angular interval
between these points is adjustable by means of the bias applied through
the secondary of the isolating transformer ahead of the rectifier. The
plate of Vi a controls the potential of the CRT cathode through d-c
restorer V la and its parallel resistor in such a way that the cathode-ray
tube is turned on only when V&, is conducting.

The range sweep and associated delay circuits are shown in the bottom
row. The simple delay multivibrator is not intended for use in range
determinations, but can be replaced by some such arrangement as that
of Fig. 13-42 if accurate range measurements are to be made.

Since only discrete sweep lengths are involved, the range-sweep
flip-flop is switched along with the sawtooth generator in order to elimi¬
nate the vacuum tube otherwise required for an automatic “turn-off”
circuit. Since the amplitude of the sawtooth is small compared to the
supply voltage, it is sufficiently linear without special precautions. If
continuous sweep-length control is desired, the circuits of Fig. 13-42
should be substituted, the feedback voltages for the turn-off circuit and
for the sawtooth generator being taken from the cathode of F 16!) .

The sawtooth passes through the “phase-splitting” amplifier Via,,
which provides signals of both polarities for the push-pull sweep ampli¬
fiers. The cathode feedback of the final amplifiers is sufficient to give
reasonably linear current amplification, since the push-pull action tends
to compensate for tube nonlinearities. The high-frequency response is
not good enough, however, to provide a linear displacement at the begin¬
ning of very fast sweeps. For this reason a “step” is introduced at the
beginning of the sawtooth by placing a small resistor in series with the
charging condenser of the sawtooth generator. The sudden transfer of
current from the switching tube Vi 5a to the condenser circuit results in
the abrupt appearance of a voltage drop across the resistor, thus providing
the step.

The above circuits can be used to produce a “micro-B” display by
the expedient of gearing together the sweep-delay and the sector-width
controls, and providing the proper normalization. A given normaliza-
tion will be correct for only one sweep speed.

1 Except for this requirement, this synchro could have a single-phase rotor.

532

THE RECEIVING SYSTEM—INDICATORS

[Sec. 13-15

In applications involving extremely rapid sector scans (several scans
per second), synchros cannot be used and a variable condenser must be
substituted for the scanner synchro. The oscillator frequency must
then be much higher. No problem of sector selection is involved, since
the rapid scanning covers only a narrow sector, which is completely dis¬
played at all times.

A typical narrow-band video amplifier and a marker signal mixer
are included for completeness. Incoming video signals of 8 to 10 volts
are amplified by Ve and applied to the cathode of the CRT. The tube
V 7a provides d-c restoration to assure the proper operating level. Elec¬
tronic range and angle indices from sources outside of the diagrams can
be mixed into the double cathode follower V 9 and applied to the CRT grid.
It is assumed that both range and angle indices have positive polarity
and that the potential of the angle-index lead is zero in the absence of a
signal.

If the center of the sector is fixed in azimuth, a great simplification can
be brought about by driving amplifier V t , V g directly from a potentiom¬
eter which replaces the remainder of the top row in the diagrams. The
azimuth blanking circuit (Vn, Vg, P 9 ) can also be replaced by a simple
cam-and-switch arrangement. If the scanner executes only a sector
scan, even this is unnecessary.

13-16. Plan-position Indicator.— As has been indicated in earlier
sections (e g., Sec. 12-2), PPI displays can be produced by any of several
methods, which, in general, may be classified under three principal
headings.

1. The rotating-coil method, in which the range-sweep current is
passed through a coil which is rotated about the tube neck in
synchronism with the antenna motion. If “off-centering" is
desired, it is provided by means of a fixed coil outside of the moving
one.

2. The “resolved time base” method, in which a sawtooth waveform
is passed through a 2-phase resolver, 1 practically always a synchro,
and the resulting sweep “components” are utilized to energize
orthogonal deflecting coils or plates.

3. The method of “pre-time-base resolution” in which slowly varying
sine and cosine voltages obtained from a d-c excited sinusoidal
potentiometer or by rectification of signals from an a-c resolver are
used to generate the necessary sawtooth. This method is used
principally in cases where the scan is too rapid for the rotating-coil
method and the antenna is so far away that the transmission of the

1 In some cases a 3-phase synchro is used, and the resulting signals are passed
through a resistor network which reduces the three phases to two.

(O Sawtooth

(A) CRT switching ~| I I I I

Ground

(b> xcrinj <*> ca,h ° de ° f ^

r Lr Lr

Cutoff

Iron-cored
off-centering coil (

Sweep coil , ~\ N
Scanner /

Synchro

534

THE RECEIVING SYSTEM—INDICATORS

[Sec. 1316

slowly varying voltages is appreciably easier than would be the
case with the sawtooth waveforms involved in the resolved-time-
base method.

Methods 2 and 3 can be applied either to magnetic or to electrostatic
cathode-ray tubes, but, because of their inferiority for intensity-modu¬
lated displays, the latter tubes are seldom used.

The Rotating-coil Method .—Figure 13-44 illustrates the circuits used
to produce the sweeps of a rotating-coil PPI, omitting such accessory
parts as range-marker circuits, etc. The tubes Vi, Vi, V and P< con¬
stitute a square-wave and a sawtooth generator similar to those of Fig.
13-42 except that a diode clamp (FjJ is illustrated for variety in Fig.
13-44. Tubes V s, a , V 5!> , and V 6 constitute a feedback amplifier whose
linear output current drives the deflection coil. The drop across the
cathode resistor of V e , which is due almost entirely to the deflecting
current, is fed back to the cathode of Fso- Because of the high gain in
the feedback lodp, this voltage faithfully reproduces the form of the
original sawtooth, thus assuring the desired linear increase in the current.
Since any current through F 6 between sweeps would result in a circular
rather than a point origin for the sweep, this tube is biased beyond cutoff.
Since there is no feedback so long as F 6 is beyond cutoff, its grid is ele¬
vated very rapidly at the beginning of the sawtooth and there is thus no
appreciable delay before the current starts.

The deflecting coil is rotated by a mechanical repeater such as those
described in Sec. 13-5. The diagram at the upper right illustrates one
method of connection for an “off-centering” coil.

This type of PPI can be made to have the greatest dependable accu¬
racy attainable with any type of intensity-modulated display. Mechani¬
cal repeater systems can, within certain limits of rotational speed, be
made to have accuracies of a sfnall fraction of a degree, 0.1° being a
common error limit. Since the range-sweep feedback amplifier is
extremely faithful at little cost, the burden of accuracy in range falls on
the sawtooth generator, for which precision parts of high constancy can
easily be used. The principal disadvantages of the rotating-coil method
are: (1) it is limited to continuous scanning rates of 30 to 60 rpm and to
sector scanning of comparable angular velocity; (2) off-centering is
extremely expensive in power, and cannot be used for displacements of
more than two or three tube radii because of excessive distortion and
defocusing; (3) for cases demanding minimum weight, even at the expense
of accuracy, the rotating-coil PPI is less suitable than some other types.

13-16. The “Resolved Time Base” Method of PPI Synthesis. —A PPI
'can also be derived by passing a sawtooth waveform through a 2-phase
resolver and using the resulting sine-and-cosine-modulated signals, with

Sec. 13 16]

RESOLVED TIME BASE PPI

535

or without amplification, to drive an orthogonal deflecting system (Fig.
13-45). When amplifiers are used, or if an electrostatic tube without
amplifiers is involved, the resolver must deliver sawtooth voltages into a
high-impedance load; when a magnetic tube is used without amplifiers,
sawtooth currents must be delivered to an inductive load.

In principle the resolver may be a synchro, a potentiometer, or a
condenser; a synchro is far the most satisfactory and, in spite of certain
shortcomings, it is universally used.

As in all cases of transmission of a nonsymmetrical signal through an
a-c coupling, the d-c component of the signal is lost. This presents one

Sawtooth

generator

Amplifier

Waveform
A or Ai

Waveform
B or B l r
c-1

| Amplifier [ ^

L__I

j- 1 -

i Amplifier 1

1_I-

CRT

J"l

A Primary signal

(unbalanced) Jl/l/L/l/L

_MAMWl

B (?o°clatring) na '

Fig. 13-45.— Resolved-sweep PPI methods.

of the most serious difficulties involved in this technique. With a passive
and linear load, the long-time average of both the current through the
secondary of the synchro and the voltage across it must be zero (Wave¬
form B, Fig. 13-45). Thus the absolute current or voltage at the begin¬
ning of the modulated sawtooth will not be constant, but will change
with the modulation amplitude and will reverse sign when the sawtooth
does. As a result, if no corrective measures were taken, each individual
sweep on the display tube would be displaced in the negative direction
by a fixed amount and the locus of the sweep origins would be a “nega¬
tive” circle. This difficulty has been overcome by two general methods,
each of which has variations most suitable to particular circumstances.

536

THE RECEIVING SYSTEM—INDICATORS

[Sec. 13-16

The first method involves the use of clamps or switches in the second¬
ary circuit to force the potential or the current to zero in the interval
between sweeps. So long as the sweep component has a given polarity,
this can be very simply accomplished in the potential case by a d-c
restorer (Sec. 13 9), and in the current case by a selenium rectifier in series
with the secondary circuit. In cases where the scanning is confined to
90° or less, these variations of the first method are the most satisfactory
of all. If the scan covers more than 90°, one of the diodes must be
switched in polarity from time to time—for example, by a cam arrange¬
ment on the scanner. If the scan covers more than 180° both of them
must be so switched. Although it is difficult to switch quickly and
smoothly enough to avoid aesthetically displeasing display irregularities,
this method is quite satisfactory and is probably the simplest for the case
of resolved currents, providing the scanning rate is not too high. A
better and only slightly more expensive method of voltage restoration
involves the use of a double clamp (Fig. 13-25) which connects the
secondary to a point of proper potential between sweeps but releases it
when the sweep begins. This is the most widely used method in the
voltage case when polarity reversal is involved. No satisfactory series
switches exist for analogous use with resolved currents.

In the second method of correcting the sweep-origin difficulty, the
positive and negative waveforms are “balanced” about the sweep origin
either by introducing a precisely controlled negative waveform in the
primary circuit between sweeps, or by arranging to trigger the trans¬
mitter automatically at the precise time when the secondary current or
voltage passes through zero. Both variations involve a good deal of
precision and are more costly than the switched clamps mentioned in the
last paragraph as usable when voltage is involved. However, the
present methods have been widely used in connection with resolved
currents, since they require no switching elements in the low-impedance
secondary circuit.

Applications of these various methods will be described in connection
with the following specific examples.

Magnetic PPI Using Amplifiers .—Figure 13-46 shows the secondary
circuit of a magnetic PPI of the resolved-time-base type using the
method of clamping between sweeps. It is supposed that the synchro
is preceded by the sweep generator and amplifier of Fig. 13-44, except
that the circuit of Fe is changed as indicated so that the feedback voltage
is that across the synchro itself.

The clamps on each of the amplifier grids of Fig. 13-46 are of the
double-triode variety illustrated in Fig. 13-25a. They are switched by
the same flip-flop (rectangular-wave generator) that controls the saw¬
tooth generator,, and are thus closed during the entire interval between

538

THE RECEIVING SYSTEM—INDICATORS

[Sec. 13-17

sweeps. The switched clamps shown can be replaced by simple d-c
restorers if the scan covers less than 90°. The final sweep amplifiers are
of the cathode-feedback type used in the B-scope of Fig. 13-43.

The centering of the PPI can be adjusted by setting the potentiom¬
eters controlling the clamping points. If extreme off-centering moves
the amplifier grids out of their normal operating range, a delay occurs at
the beginning of the sweep which gives the effect of a virtual center at the
desired point. By using an extremely high-voltage sawtooth, off-center¬
ing of as much as six to eight tube radii has been provided. For such
extreme amounts of off-centering, it is best to insert cathode followers
between the potentiometers and the clamps.

The dependable accuracy obtainable with the resolved-time-base
method is not so great as can be obtained with a rotating-coil PPI,
although with care it can be made nearly as good except on very fast
sweeps. However, the present method has much less severe limitations
with respect to scanning speed, and provides a much greater degree of
usable off-centering than does the rotating-coil scheme.

Its weight is somewhat less and its power requirements somewhat
greater than those typical of the rotating-coil variety without off-
centering. When off-centering must be provided, the present method is
far lighter and less costly in power.

The technique just described can be applied to electrostatic tubes
by substituting voltage amplifiers in the final driving stages, or in some
cases by eliminating amplifiers entirely and connecting the clamped
points directly to one member of each pair of deflecting plates. Unless
weight and power consumption are extremely critical, the saving effected
does not justify the sacrifice in quality entailed.

13-17. Resolved-current PPI. —When the deflection coils are driven
directly by the synchro, the amplifiers of Fig. 13-46 are eliminated, with
the result that the indicator is considerably simplified and errors due to
imperfections in the amplifier response are avoided. These advantages
are accompanied by certain restrictions which will appear below.

In order to reduce the effects of distributed capacity in the synchro
and the deflecting coils, and of the shunt capacity of the cables, low-
inductance windings of few turns are used throughout. The synchro
rotor is matched to the driving tube by a stepdown transformer. Since
the secondary circuit is almost purely inductive (ideally it would be
precisely so), its current waveform will resemble that in the primary of
the transformer, and a current amplifier similar to that driving the deflec¬
tion coil of Fig. 13-44 is appropriate. In many cases imperfections in the
transformer are overcome by taking the feedback from its secondary
circuit.

The low deflection sensitivity of the sweep coils renders it impractical

Sec. 1317]

RESOLVED-CURRENT PPI

539

to use them for off-centering; therefore, when this is desired, separate
coils are provided on the same form. Since they are inductively coupled
to the sweep coils, the number of turns in the off-centering coils must also
be limited. Off-centering is therefore expensive in current, and its
extreme amount is usually limited to not more than two tube-radii.

Since vacuum tubes are not appropriate as switches in such low-
impedance circuits, it is not possible to fix the sweep origin by methods
analogous to that of Fig. 13-46. It has been necessary to use either the
method of a series dry-disk rectifier switched (if necessary) by the scan¬
ner, or to apply some method of waveform balance. Applications of
these methods appear in the following descriptions.

The Use of Series Rectifiers .—Figure 13-47 illustrates those parts that
must be added to the sweep generator and amplifier of Fig. 13-44 to
produce a complete PPI involving the use of disk rectifiers. By provid-

Fig. 13-47.—Resolved-current PPI using switched rectifiers.

ing two rectifiers for each secondary as indicated, only one point need be
switched. Optimum smoothness at the instant of switching is accom¬
plished if contact is made through the second rectifier before the first
one is opened, so that the circuit is never broken.

This method has the virtue of extreme simplicity and in many cir¬
cumstances it gives excellent performance. However, it has two princi¬
pal limitations in addition to the restriction on off-centering mentioned
above: the mechanical switching limits the scanning rates at which it can
be used, and some distortion is introduced on “long” sweeps (more than
50 miles) by the low but appreciable resistance of the rectifiers. If this
resistance were constant, the only effect would be a droop caused by
inadequate low-frequency response. This droop could easily be over¬
come by shaping the primary waveform, but unfortunately the rectifier
resistance is nonlinear, being much larger at very low than at intermediate
or high currents. As a result, the effect of the rectifier resistance changes
with scan angle. “Circles” of equal range are slightly “squared,” the
“corners” coming at the 90° positions. 1

1 This effect should not be confused with the “square circles” found on certain
early PPI’s of the type shown in Fig. 13-46. These errors, which resulted from

540

THE RECEIVING SYSTEM—INDICATORS

[Sec. 1317

Automatic Triggering of the Transmitter. —Wavefom balance by trigger¬
ing the transmitter as the secondary current reaches zero is illustrated
in Fig. 13-48. Since the voltages in the secondary circuits are low, the
signal from the cathode resistor in the sweep amplifier is used to provide
the required information. This signal is passed through a network whose
voltage response is equivalent to the current response of the deflection-
coil circuit, and from there to the first stage of a high-gain amplifier. The
grid of the first amplifier tube is so biased that in the absence of signal it

A and B

Fio. 13-48.—Resolved-current PPI using automatic transmitter triggering.

is exactly at cutoff. Thus when a sweep is being applied this grid will
pass upward through its cutoff ppint at exactly the same time that the
deflecting current is passing through zero. The remainder of the saw¬
tooth is therefore amplified and, by suitable overdriving and clipping, can
be turned into a rectangular wave. The transmitter trigger is then
derived from the front edge of this rectangular wave, and the wave itself
serves to intensify the cathode-ray tube.

If a simple saw-tooth is used, the maximum useful sweep duration has
an upper limit of half the pulse period; somewhat less can be realized in

inadequate high-frequency response in the synchro and amplifiers, and from cross¬
coupling in the former, were troublesome only on fast sweeps. Furthermore the
“corners” were at the 45° rather than the 90° positions.

Sec. 1317]

RESOLVED-CURRENT PPI

541

practice because of the finite time for sweep “recovery.” By using a
trapezoidal waveform, in order that the time spent at maximum “nega¬
tive” current become appreciable, sweep duration can be increased to
about 60 per cent in practice. This is easily accomplished through the
medium of a resistor in series with the integrating condenser of the saw¬
tooth generator, as is explained in Sec. 1314.

This form of resolved-current PPI has been successfully used in the
lightweight airborne equipment (AN/APS-10) described in Secs. 15T2
to 15T4. As is shown in Fig. 13-48, the synchro is driven directly by the
amplifier without a transformer. The synchro secondary and the deflec¬
tion coil (which is wound in a standard synchro stator form) have 3-phase
rather than 2-phase windings. The equipment is light in weight, com¬
paratively simple and economical. Its principal drawbacks are the
limited duty ratio, the precision required in the triggering circuit, and
the limited off-centering attainable. No off-centering is used -with the
3-phase system of Fig. 13-48; when
it is desired, 2-phase windings are
more suitable.

The Use of Special Waveforms.

The method that will now be de¬
scribed is similar to that just
treated in that positive and nega¬
tive signals are “balanced.” It
differs, however, in that the wave¬
form includes a quiescent period,
immediately preceding each
sweep, during which the waveform
has its average value, so that
there is no necessity for precise
control of the trigger (Fig. 13-45).

The required waveform in the pri¬
mary is derived by the introduc¬
tion, immediately following the
sweep proper, of a signal of opposite polarity whose time integral is
exactly equal to that of the sweep. Both sinusoidal and rectangular
waves have been used, but only the former will be discussed here.

A waveform of the proper type can be generated by the Miller-type
circuit (Sec. 13-10) shown in Fig. 13-49. When the grid of Vi is released
by opening the switch, it quickly rises to cutoff and a negative sawtooth
begins on the plate. The form of this wave is practically independent of
the load impedance, which is in this case made up of the inductance L, V 2 ,
and R 2 in series, and the various capacities. The a-c component of cur¬
rent in the coil is at any instant given by

Fig. 13-49.—Balanced-waveform generator
using an inductance.

542

THE RECEIVING SYSTEM—INDICATORS

[Sec. 13-17

and is therefore proportional to the time integral of E. When E reaches
the desired maximum value, the switch is closed and V 1 is disconnected.
The sudden termination of its current results in an oscillation of L and its
associated capacity. The plate end of the inductance swings positive,
disconnecting F 2 as the potential rises past the 200-volt level. On the
down-swing, F 2 becomes conducting again and clamps the inductance to
the 200-volt point, resulting in the waveform shown. The amplitude of
the oscillation is dependent upon the energy stored in the inductance at
the end of the sawtooth, which in turn is determined by the current and
hence by the “area” under the sawtooth. It can be rigorously proved
by analysis that this amplitude must be such that the average voltage
across the inductance (neglecting its resistance) is zero during the wave¬
form. We shall be content with the general statement that this must
be so since, in the absence of resistance, the average potential across
an inductance during a completely closed cycle must be zero regardless of
waveform. Therefore in this case the initial, the average, and the final
values of the waveform are identical and it is “balanced” as desired.

A complete circuit using this method is illustrated in Fig. 13-50. The
Miller circuit is switched by the double-diode clamp V 3 , V<, which in turn
is controlled by the cathode-coupled flopover Vi, Vi. The latter is
automatically terminated at a fixed sawtooth amplitude by the signal
passed through the biased diode F 8 . The Miller circuit is like that
described in connection with Fig. 13-49, except that V 7 (Fj of Fig. 13-49)
is biased somewhat below 200 volts, thereby introducing a small correc¬
tion to take care of inadequacies in the response of the deflection system.
The potentiometer Pi allows a wide variation in the sweep speed used,
and P 3 adjusts the pattern to proper size.

The amplifier uses negative feedback of a signal taken across a resistor
in the transformer secondary, thereby correcting for deficiencies in trans¬
former response. In contrast to previous cases, the final stage of the
amplifier is driven negative during the actual sweep; thus the induced
voltage on the plate is positive and the tube does not “bog down.” The
high potential needed for quick recovery when the current is rising again
is provided by the joint action of L 1 and C 1 . During the sawtooth a large
positive voltage is induced in L\, and Ci is charged accordingly. When
the current derivative reverses at the end of the sawtooth, the voltage is
temporarily maintained at a high level by C 1 , and, in spite of the induced
voltage across the transformer, the plate of the tube remains at a work¬
able voltage level during the rapid back-swing. The choice of polarities
is such that the interval in which C 1 aids the plate supply is short.

nuie.

All parts
resistors
otherwise

: 10% and all
watt unless
specified

—==—•- Intensifying
_l L_ gate to CRT

Rectangular Area - balanced sweep

waveform waveform generator

generator

Fig. 13-50.—Balanced

PPI.

Feedback

amplifier

RESOL

544

THE RECEIVING SYSTEM—INDICATORS

[Sec. 13-18

The performance of this type of PPI is comparable to that in which
the transmitter trigger is generated automatically. Technically, it
involves fewer parts, its method of area balancing has somewhat greater
reliability, and it has the advantage of being usable with self-synchro¬
nous modulators. In common with all balanced-waveform methods, its
duty ratio is limited to some 50 to 60 per cent unless excessively large
peak currents are used in the balancing waveforms.

13-18. The Method of Pre-time-base Resolution. —In certain cases
it is desirable to transmit the scanner data in terms of slowly varying
sine and cosine voltages derived from a sine-cosine potentiometer, or by
the modulated-carrier technique used in the B-scope of Sec. 1314. These
are used as potential sources for sawtooth generators, as indicated in
Fig. 13-51, where the switches represent double-sided clamps that are

Fig. 13-51 .—Pre-time-base resolution method of PPI synthesis.

opened during the sweep interval. Thus the signals at the input to the
amplifiers are sine-and-cosine-modulated sawteeth of precisely the same
nature as those obtained by passing a sawtooth through a synchro. The
amplifiers can, therefore, be identical with those of Fig. 13 46. If it is
too inconvenient to provide both polarities, one can be omitted in each
circuit and a phase-inverting amplifier inserted between the sawtooth
generator and the final amplifiers. In this case, however, it will be neces¬
sary either to use d-c coupling (which is difficult) or to provide clamps on
the grids of the final amplifiers.

This method can be used at very high scanning speeds, since it is
possible to use a variable condenser for carrier modulation. It has
advantages over the resolved-time-base methods when very fast sweeps
are used, since there is no starting delay such as that introduced in passing
sweeps through a synchro. It can also be advantageously used when the
scanner is so remote as to make the transmission of sweep signals by
cable difficult, and when the scan is at the same time too rapid to permit

Sec. 1319]

THE RANGE-HEIGHT INDICATOR

545

the use of mechanical repeaters. An extreme case is that of radar relay
(see Chap. 17). Many of these advantages make the technique par¬
ticularly appropriate for use on range-height indicators.

On the other hand, under average conditions, pre-time-base resolution
is considerably less satisfactory than the methods previously described.
The sine potentiometer, though simple, is prone to troublesome irregu¬
larities which cannot be completely filtered, except on extremely slow
scans, without causing phase lags in the basic scanner data. The use of
a carrier and of demodulators introduces considerable complexity com¬
pared with methods described earlier. The necessity of maintaining the
sawtooth generators in proper normalization in order to avoid distortion
is somewhat of a burden compared to other cases where only one such
generator is involved and where, furthermore, any lack of constancy
affects only the size and not the fidelity of the display.

13-19. The Range-height Indicator. —Any off-centered PPI can be
used as a range-height indicator by substituting elevation angle for
azimuth, providing the indicator can follow the scanner involved. In
most cases, it is desirable to present height on a scale that is considerably
expanded in comparison to that used for the display of ground range.
In consequence the most adaptable PPI techniques are those in which
each cartesian coordinate has its own amplifier which permits the desired
height expansion to be provided simply by increasing the gain of the
proper channel. The methods of Figs. 13-46 and 13-51 can both be used
in this way.

Simplification can usually be effected. The horizontal sweep always
occurs on the tube face in one direction from the origin. In many cases,
this is also true of the vertical component. (Sometimes negative heights
are involved when the radar is on an elevated site.) Furthermore, it is
often possible to use one or both of the approximations sin 9^9 and cos
9 ~ 1. In any case in which a sweep component is unipolar, the clamps
of Fig. 13 46 can be reduced to unswitched d-c restorers, and the switched
clamps of Fig. 13-51 can become single-sided, though still being switched.
The approximation cos 9 ~ 1 allows the use of unmodulated sweeps in
the horizontal direction; this is of no particular virtue if the resolved-
sweep technique is used, but provides a considerable saving in connection
with the use of a modulated carrier. The approximation sin 9 ~ 9 allows
the use of linear data transmitters, such as linear potentiometers and
condensers.

Since the applications of Fig. 13-46 and Fig. 13-51 to use with an
RHI are fairly obvious, no attempt will be made to discuss them specifi¬
cally. Instead, a brief description will be given of an RHI for use with
rapid scans including the “sawtooth” type developed by certain electrical
scanners (Secs. 9-14, 9-15, and 9-16). It is assumed that sin 9^9 and

UlJULr vlTML/L

Fig. 13-52.—Range-height indicator for rapid-scan system.

546 THE RECEIVING SYSTEM—INDICATORS [Sec. 1319

Sec. 13-19]

THE RANGE-HEIGHT INDICATOR

547

cos 6 — 1 are sufficiently good approximations. In Fig. 13-52, informa¬
tion for the vertical sweep is derived by modulating a high-frequency
oscillation by a variable condenser, using the voltage-dividing circuit of
Fig. 13-7. This is peak-detected by the cathode follower Fi, whose
cathode circuit has a time constant that is long compared with the
period of oscillation. The cathode and grid of Fi are so biased that
the former is at ground potential in the absence of signal. The demod¬
ulated voltage controls a sawtooth generator of the ordinary type, thus
providing sawteeth modulated in proportion to the elevation angle.
These are passed through a phase splitter and a push-pull amplifier to
the vertical deflecting coils. Since the sweep is always in the same

Fig. 13-53.—V-beam height indicator.

direction, d-c restorers provide adequate clamping on the output stages.
The horizontal sweep, of constant amplitude, is generated in the ordinary
way and amplified as was the vertical one. Off-centering is provided
by proper biasing of the driver tubes. A delay can be used in the
horizontal circuit to allow a distant range interval to be examined in
detail. (If this is not a requirement, the same flip-flop can be used for
both sawtooth generators.) A controllable height marker can be
derived, if desired, by applying the modulated sawtooth to a biased-diode
delay circuit, as explained in Sec. 1312.

V-beam Height Indicator .—In the F-beam height indicator (Fig.
13-53), a linear potentiometer turned by a mechanical repeater provides
the azimuth data, a differential gear allowing control of the sector
displayed. The vertical deflection is obtained by adding, in the driving
amplifiers, a slowly varying voltage proportional to the azimuth angle
measured from the edge of the sector chosen and a range sweep modulated

548

THE RECEIVING SYSTEM—INDICATORS

[Sec. 13-20

by the same azimuth voltage. The horizontal sweep is unmodulated but
arranged to permit delay in discrete steps. Height is read from an
engraved scale as explained in Sec. 6-12. If several scales are to be used
in connection with delayed sweeps, the reflection method of Fig. 7-4 is
used.

SIGNAL DISCRIMINATION, RESOLUTION AND CONTRAST

The factors that influence the discernibility of a simple radar echo
signal against thermal noise have been discussed in Chap. 2 and in the
early sections of Chap. 12. We have seen that the characteristics of
the receiving equipment which influence this matter most profoundly
are the noise figure and bandwidth of the receiver, the integrating
properties of the cathode-ray tube screen, and the type of display. To a
lesser extent the cathode-ray-tube spot size and the scale-factor of the
display also play a role. Section 12-8 points out methods of increasing
the signal discernibility in the presence of various forms of radiant
interference by taking advantage of differences between the desired
and the undesired signals, and shows that to some extent these same
techniques aid in distinguishing a point target from more diffuse ones.
Chapter 16 describes an extremely elegant method by means of which
a given target can be readily distinguished from its surroundings, pro¬
viding it is in motion with respect to those surroundings and that they
are at rest or have a uniform mass motion.

The following paragraphs will discuss another aspect of the discrim¬
ination problem—that of the presentation of a multiple or complex
picture when it is not desired to suppress any of the information but
rather to present it in as detailed a manner as possible.

13'20. Resolution and Contrast. —In order to distinguish between
objects or among different parts of the same object it is necessary that
they be resolved. The characteristics of the receiving equipment which
influence resolution are the bandwidth of the signal channel, which
affects range resolution, and the spot size and scale factor of the display,
which also affect range resolution and to a lesser extent angular resolution
as well. Since factors concerned with the display are least under control,
and since their limitations often fix the limit of useful bandwidth, they
will be discussed first.

The spot size of a cathode-ray tube depends upon the tube type,
the performance of the individual tube, the voltage employed, the
design of focus and deflecting coils, and the intensity level at which
the tube is operated. In the series of magnetic tubes used for radar,
spot size is roughly proportional to the tube radius and is usually such
that between 150 and 200 spots can be resolved along the display radius.

In this discussion, the number of resolvable spots in a radius will

Sec. 13-20]

RESOLUTION AND CONTRAST

549

be taken as 180. On a range sweep of length R nautical miles, the
number of radar pulse lengths resolvable in principle is 12-2 R/t, where r
is the pulse length in microseconds. Thus, on a centered PPI, the
fundamental pulse-length resolution and the spot-size resolution are
equal when 12-2 R/t = 180, or R ~ 15 when r = 1. Accordingly, on
a set with a 1-^sec pulse, a 15-mile centered PPI will have the full inherent
range resolution; a 100-mile PPI will reduce it approximately sevenfold,
and so on. This reduction in resolution can be overcome by the use of
expanded displays, but often this measure restricts the field of view.

Fortunately for the indicator designer, however, this is not the
entire story. For one thing the operator cannot, except on the fastest
sweeps, realize the fundamental range resolution without optical aids
even if the display were to make it available; indeed, on a 5-in. tube
the spot-size resolution for a 100-mile sweep is nearly as good as can be
comfortably used, although on a 12-in. tube it is three or four times
worse. Second, range resolution alone is of limited usefulness if it is
accompanied by poor angular resolution; here the fundamental limitation
is usually not the indicator but the azimuthal beamwidth. The angular
width of the CRT spot on any PPI is given in radians by R/180r, where R
is the radius of the tube and r is the distance from the range origin to
the spot in question. This width will be equal to the beamwidth 0,
measured in degrees, when 57/£/180r = 0 or R/r = 30. Thus, even
for a 1° beam, the display resolution exceeds the fundamental resolution
for all points farther from the origin than one-third of a tube radius.
The cathode-ray tube is usually not the limiting factor in over-all angular
resolution, although in certain cases of accurate range measurements or
of observations on groups of aircraft or ships at long range, better range
resolution on long-range displays would be useful. Frequently, however,
the need for high dispersion requires expanded displays quite apart from
question of resolution.

The above discussion shows that in general the cathode-ray tube
imposes a severe restriction in range resolution on any but the fastest
sweeps. It is therefore apparent that unless fast sweeps are to be used
there is no point in going to extreme bandwidths in the receiver. In
most cases the receiver bandwidth need not be so great as to impair
seriously the signal-to-noise discrimination. It should be borne in
mind, however, that with too small a bandwidth, a signal far in excess of
the limit level has a much greater duration after limiting than has a
weak signal.

Contrast .—The contrast of the display depends upon the character¬
istics of the screen and upon the way in which it is excited. Unfortu¬
nately present tubes of the persistent type have serious shortcomings in
contrast. The screen material has a natural color much like that of the

550

THE RECEIVING SYSTEM—INDICATORS

[Sec. 13-21

phosphorescent light, so that contrast is reduced by reflected light. The
necessary thickness of the screen tends to blur the edges of the signals
and thus reduce contrast gradient, as do also limitations in the sharpness
of focus of the electron beam. Many screens also have a certain amount
of graininess which contributes to the reduction of contrast gradient.

Contrast between signals of different intensities is especially impor¬
tant in overland flying, where it is essential to be able to distinguish land
from water and at the same time to have good contrast between weak
echoes from ordinary terrain and the much stronger ones from built-up
areas. Unfortunately the range of echo intensities involved is so great
that, if the receiver has gain high enough to render the terrain visible,
the signals from built-up areas must be drastically limited to avoid
“blooming” of the cathode-ray tube, and detail is destroyed. If the
gain is low enough to preserve detail, the land background is not visible.

This difficulty is made worse by the nonlinear response of the cathode-
ray tube. As was previously mentioned, the beam current in a magnetic
tube is proportional to the cube of the grid-voltage swing measured from
cutoff, which is the operating point in the absence of signal. This
means that a signal of, for example, half the voltage of a limited signal
will, in principle, give only one-eighth as much light intensity. In actual
fact the difference is not so great as this, because of the tendency of the
screen to saturate on strong signals. This nonlinearity reduces con¬
siderably the difference in voltage between those signals that are just
strong enough to produce a visible result and the level at which strong
signals must be limited. It is possible to introduce a nonlinear element
in the video amplifier to compensate for the tube characteristic, and this
has been done with some success. No really satisfactory circuit of this
sort has been devised, no doubt because the need for it was fully appre¬
ciated only recently. Even with a linear CRT grid characteristic,
the problem of narrow dynamic range would be a serious one. General
methods of attacking it will now be described.

13-21. Special Receiving Techniques for Air-to-land Observation.—
Some improvement in the ability to distinguish land from water and
at the same time to see detail in built-up areas can be effected by using
the anticlutter techniques described in Sec. 12-8. Fast time constants,
instantaneous automatic gain control, and other such circuits tend to
suppress saturation on long blocks of signals and to make full use of
changes in the signal intensity. Unfortunately the use of such measures
results in an unnatural appearance of the display which makes inter¬
pretation exceedingly difficult. Shorelines, for example, stand out
very strongly, as do changes in the terrain. Similarly a solidly built-up
area appears chiefly in outline, with other strong signals at points of
changing signal intensity. Consequently, although they are extremely

Sec. 13-211

552

THE RECEIVING SYSTEM—INDICATORS

[Sec. 13-21

Fig. 13-55.—Effect of three-tone PPI. (a) AN/APS-15 scope photo of Boston without
three-tone; ( b ) AN/APS-15 scope photo of same area with three-tone.

Sec. 13-21]

SPECIAL RECEIVING TECHNIQUES

553

valuable for certain purposes, anticlutter measures leave much to be
desired in the situation under discussion.

The “Three-tone” Method .—A simple but extremely effective method
of retaining detail on high-intensity echoes while still providing land-to-
water contrast is illustrated in Fig. 13-54. At some point in the receiver,
ahead of any saturation or limiting, the signals are split into two channels,
in one of which they are amplified much more than in the other. If the
signals are not already in video form, each channel includes a detector.
In any case, each contains a limiter, the one in the low-gain channel
being set at approximately twice the level of the other. The two sets of
signals are mixed beyond the limiters and then passed through a standard
video amplifier. As the waveform diagrams show, the result is to
enhance the strength of the land echoes without destroying the detail

in those from the built-up areas. A “before and after” picture is shown
in Figure 13-55.

Many variations of this technique are possible. One, which has
been applied to existing sets in which an additional channel is difficult
to install, consists of switching the gain up and the limit level down on
alternate pulse cycles by means of a scale-of-two multivibrator, the
results being added on the cathode-ray-tube screen. The results are
almost indistinguishable from those obtained by the use of two channels.

The Logarithmic Receiver .—A more involved method of increasing
the dynamic range of the system is by use of the so-called “logarithmic”
receiver, whose gain characteristics are such that the response varies
approximately as the logarithm of the input signal. One method of
attaining such a response, which is actually an extension of the three-tone
method, is illustrated in Fig. 13-56. At low signal levels the principal
contribution is from the last stage, where the over-all gain is highest.

554

THE RECEIVING SYSTEM—INDICATORS

[Sec. 13-21

As the signal level increases, the last stage saturates and can contribute
no more. By this time, however, the contribution from the preceding
stage has become appreciable and the output continues to increase,
but at a lower rate than that occurring when the gain of the last stage
was included. Eventually the second stage saturates, and the gain
drops to that from the next preceding stage, and so on. Thus the total
signal range is compressed, but there is no complete saturation even on
very strong signals. Such receivers have not had very extensive tests
with conventional airborne radar, but the rather meager results have
shown promise. One variant that has not been tried, to the author’s
knowledge, is to use different saturation (or limit) levels in the various
channels, as in the three-tone method, making this a “multi-tone”
device.

CHAPTER 14

PRIME POWER SUPPLIES FOR RADAR

By M. M. Hubbard and P. C. Jacobs

Radar equipment requires for its operation high-voltage (1000- to
10 ,000-volt) direct current, medium voltage (300- to 600-volt) direct
current, and power for vacuum-tube heaters which usually can be either
alternating or direct current. Normally, the desired d-c voltages are
obtained from an a-c supply by the use of transformers and rectifiers,
either of the thermionic or of the dry-disk type. Power supply design
varies with the application, and differs for aircraft installations, ground
system installations, and ship installations.

AIRCRAFT SYSTEMS

Radar power in aircraft should, if possible, be obtained from directly-
generated alternating current. Where this is not practicable, means exist
to convert low-voltage direct current from the aircraft electrical system
to the desired type of supply voltage.

Table 141.— Recommended Power Sources

Radar load, watts

Recommended
radar power source

Alternate

choice

Less than 150.

150-250.

Vibrator

400 cps 1 </> motor-alter¬
nator

Dynamotor

Dynamotor'

250-750.

Direct engine-driven
1<£ alternator 400 cps
or higher

400 cps l</> motor-alter¬
nator

750-10,000.

Direct engine-driven
3 <f> alternator 400 cps
or higher

For ranges up to
watts, 400 cps
motor-alternator

2300

Aircraft electrical systems today are normally 12-volt or 24-volt
direct current. A few aircraft have 110-volt d-c supply. Ratings are
nominal; a “24-volt” aircraft system usually supplies 27.5 ± 2.0 volts.

14*1. Choice of Frequency. —One of the most controversial points in
early radar development was the selection of the a-c frequency to be
used as primary radar power. A transformer correctly designed for the
frequency / will behave tolerably at frequencies up to 3/, but will burn

555

556

PRIME POWER SUPPLIES FOR RADAR

[Sec. 14-1

up at a frequency of f/2. The general equation for induced voltage in
a transformer

„ , d<t>

E = k ■ n ■ -r-
at

(1)

gives, for a fixed core area,

E , , . dB

E = k ■ 11 ■ A —rr 7
at

(2)

where k is a constant, n the number of turns in the winding considered,
<t> the flux linking these turns, A the area of the core, and B the magnetic
induction in the core. For sinusoidal voltages of frequency/,

E m „ = k ■ n ■ f ■ A • Bmn. (3) •

Thus if / is halved, B„... must double for a fixed input voltage, all
other terms being constant in any given case. Since losses in the iron
are a function of 5^,, doubling B mxx produces an immense increase in
magnetizing current and in core loss. The core area and thus the weight
of the transformer as a whole can be decreased as / increases because of
the corresponding reduction in B m „. By going from 60 cps to 400 cps,
savings in transformer weight of 50 per cent are attainable. Core area
cannot be much further reduced by increasing / from 400 cps to 800 cps,
as iron losses per pound for constant increase more than linearly with
frequency. Weight savings of 10 per cent at most are obtainable by
this change in frequency.

Performance of rotating equipment must be considered, as well as
that of transformers. For stable performance and minimum weight
of alternators and a-c motors, 400 cps is preferable to 800 cps. (See
Sec. 14-2 on wave shape.) The majority of existing airborne radar sets
are designed for 400-cps minimum supply frequency, and it appears that
this will continue to be the nominal standard. Variable-frequency
alternators are also used; they commonly give a 2 to 1 ratio between
minimum and maximum frequencies, depending on the speed of the
aircraft engine. Ranges often encountered are 400 cps to 800 cps,
800 cps to 1600 cps, and 1200 cps to 2400 cps. Table 14-2 shows the
power frequencies used in Allied military aircraft during the past war.

Table 14-2.— Standard Power Frequencies

User Frequency, cps

USAAF. 400 fixed

USAAF. 400 to 800 variable

USN. 800 fixed

USN. 800 to 1600 variable

USN. 400 to 800 (3<*>) variable

1200 to 2400 variable
1300 to 2600 variable

RAF

Sec. 14-3]

DIRECT-DRIVEN ALTERNATORS

557

14-2. Wave Shape. —Since all electric power used for radar is con¬
verted to direct current or is used for heating, there is no inherent require¬
ment for sinusoidal wave shape. 1 However, an alternator furnishing
voltage of poor waveform may show very marked changes in waveform
when its load is changed. Since a stable d-c voltage is the final require¬
ment in most radar power supplies, it is necessary to maintain a fixed
relationship between the maximum voltage and the rms voltage, whose
ratio is called the “crest” or “amplitude factor.” The output d-c
voltage / or rectifier circuits employing condenser input will be a function
of the crest voltage. For rectifiers employing choke input, the ratio
of rms voltage to average voltage is important; this ratio is called the
“form factor.” These two ratios should be as constant as possible under
all load conditions. This condition is more easily met by the use of
alternators with low subtransient reactance. Practically, it is preferable
to employ conventional salient-pole rotating-field synchronous alter¬
nators designed for 400 cps, rather than high-impedance inductor alter¬
nators operating at higher frequencies. Although the reactance of an
inductor alternator can be neutralized by a series capacitance (as is done in
the Model 800-1-C Bendix 800-cps motor-alternator) such balance is com¬
pletely effective only at one value of a load exhibiting fixed power factor.
Changes in load cause changes in wave shape. Thus, even if the voltage
regulator (Sec. 14-5) behaves perfectly and maintains constant E. r or
E ram , the output d-c voltage applied to the radar may vary excessively.
(See Fig. 14T.)

Furthermore, individual machines of the inductor-alternator type
show wide variation in characteristics. Crest factors measured for
different machines of a given type have shown variations in the range from
1.15 to 1.75. When power is to be derived from an alternator of this
type, transformers for radar rectifiers should be provided with primary
taps, and filament supplies should be obtained from separate transformers.

14*3. Direct-driven Alternators. —Since all power is ultimately
derived from the rotation of the aircraft engine, fewer devices that can
cause trouble are required if mechanical rotation is used directly to
drive an alternator. A direct-driven alternator will normally furnish
alternating current whose frequency varies with engine speed. This is
usually satisfactory for radar operation. In some complex components,
such as equation-solving circuits, and for synchro applications, fixed
frequency is necessary. In these cases it is often desirable, particularly
where the a-c loads are heavy, to obtain that part of the load which can
be allowed to vary in frequency from an engine alternator, using a small
inverter set to obtain the fixed-frequency power needed.

1 One exception to this statement should be mentioned. In an a-c resonance
charge modulator, the generator must produce a good sine wave.

800 cps 0.9 PF 800 cps 800 cps PS 0.9 PF 800 cps

CF 1.71 FF 1.16 CF over 2 FF 1.24 CF 1.40 FF 1.09 CF 1.47 FF 1.12

1200 cps 0.9 PF 1200 cps 1200 cps PS 0.9 PF 1200 cps

CF 1.70 FF 1.16 CF over 2 FF 1.19 CF 1.47 FF 1.11 CF 1.62 FF 1.14

Fig. 14*1.—Voltage wave shape of Eclipse NEA-6 generator.

CF—crest factor; FF—form factor.

558 PRIME POWER SUPPLIES FOR RADAR [Sec. 14-3

Sec. 14-3]

DIRECT-DRIVEN ALTERNATORS

559

For loads approaching 1 kw, particularly in the case of systems with
heavy current demands, weight savings can be appreciable if 3-phase
generation is employed. No saving in transformer weight is usually so

Fig. 14-2. —Eclipse NEA-7 dual-voltage generator.

Fig. 14-3.—General Electric dual-output gear box and generators for 3-phase a-c radar power

and aircraft d-c supply.

obtained, but the alternator is lighter or more reliable, and filters for the
higher ripple frequency are appreciably smaller and lighter. In one
specific case, a 3-phase power supply furnishing 3-kw direct current
showed a saving of almost 70 lb over the equivalent single-phase unit.

560

PRIME POWER SUPPLIES FOR RADAR

[Sec. 14-3

In many cases, a limit on the number of engine mounting pads will
force the use of a dual-purpose generator such as the Bendix Aviation
Corporation NEA-7, which delivers 125 amp of 27.5-volt direct current
and also, independently controlled in voltage, 2500 va of single-phase,
115-volt alternating current at 800 to 1600 cps for shaft speeds of 4000
to 8000 rpm. (See Fig. 14-2.) A typical example of a large 3-phase
direct-drive alternator is the General Electric Company 10-kva 3-phase
208/120-volt 400- to 800-cycle machine shown in Fig. 14-3. This
photograph shows the installation as designed for use in TBM-3 aircraft,
using an auxiliary gear box to obtain dual output from the TBM-3’s
single engine pad. This expedient is usually much more successful than
attempting to convert (with low efficiency) direct current to large
‘‘bites” of alternating current. When pressed for output mounting-pad
space it is well to consider such “dual outlet” gear boxes. Often such
a box can be employed with older engines (2000- to 4000-rpm jack-shaft
speed) to utilize high-output 4000- to 8000-rpm alternators by incorpo¬
rating a step-up ratio in the box. Such a gear box was designed to
permit use of the same General Electric Company generator with the
low-speed jack shafts of the B-17-G aircraft engines.

Large aircraft of the future will probably have electrical systems
furnishing 3-phase 400-cps fixed-frequency power at 208/120 volts
(120-volt phase to neutral, 208-volt phase to phase). This will give
200/115 bus voltages. Preliminary tests indicate that such systems,
especially those having several large generators in parallel, will be stable,
reliable, and directly usable for radar. 1

Summary of Alternatives to Direct-driven Alternators .—If direct-
driven alternators cannot be employed in any given case, or if the power
requirements are so small as to render a special generator impractical,
there are five alternatives:

1. Motor-alternator sets. D-c motor input, 400- or 800-cps output.

2. Inverters. Same input and output as (1) but with a single mag¬
netic circuit—a true inverter.

3. Dynamotors. Low-voltage d-c input, high-voltage (or voltages)
d-c output.

1 H. E. Keneipp and C. G. Veinott, “A 40-kva, 400-cycle Aircraft Alternator,”
AIEE Transactions, 63, 816-820 (November 1944).

L. G. Levoy, Jr., “Parallel Operation of Main Engine-driven 400-cycle Aircraft
Generator,” AIEE Transactions , 64, 811-816 (December 1945).

W. K. Boice and L. G. Levoy, Jr., “Aircraft Alternator Drives,” AIEE Trans¬
actions, 64, 534-540 (July 1945).

M. M. Hubbard, “Investigation of 3-phase 208/120-volt 400-cycle Aircraft
Alternators,” RL Group Report 56-061545.

Sec. 14-4]

MOTOR-ALTERNATOR SETS

561

4. .Mechanical vibrators. Low-voltage d-c input, output direct
current or 120-cps alternating current or any combination.

5. Electronic inverters. Low-voltage d-c input, output as desired.

The options (2) and (5) can be discarded at once. Electronic invert¬
ers, although theoretically the most desirable, are practical only for
power levels of a few watts because of low efficiency arising from tube
plate-drop. Inverters are usually undesirable because they cannot be
regulated. This leaves motor-alternators, dynamotors, and vibrators.
Practical limitations on commutator diameter, voltage per bar, and
operation at altitude restrict the use of dynamotors. For example,
it is never wise to attempt to use dynamotors with outputs above 1200
volts. Motor-alternators with voltage regulators are the most reliable
conversion means.

14-4. Motor-alternator Sets.—Table 14 3 gives common sizes of
motor-alternator sets now in use.

Table 14-3.— Common Sizes oe Motor-alternator Sets

Capacity, va

Frequency of J
output, cps

Phases

Weight,

va/lb

100

400

250

400

1 or 3

19.2

500

400

21 .8

750

100

1 or 3

19.8

840* (1000)

800

32 f

26.2 (31.5)

1500

400

27.2

2500

400

33 4

* 840 is nameplate rating. For operation below 10,000 ft with blast cooling, 1000 va are obtainable,
t Includes weight of external r-f filter and 12-^f series condenser. See Figs. 14-8, 14-16, 14 17, 14 21
for pictures of some commonly used 400-cycle motor-alternators.

For heavy-current duty, particularly at high altitude, brush wear
becomes a problem. Care should be taken to see that all rotating
devices using brushes requiring operation at altitudes above 20,000 ft
have suitable “high-altitude” brushes. 1

Starting currents are often a serious problem in the case of motor-
alternator sets rated at 750 va or more since they may be 5 to 10 times

1 L. M. Robertson, “Effect of Altitude on Electric Apparatus,” Electrical Engineer¬
ing (June, 1945).

Paul Lebenbaum, Jr., “Altitude Rating of Electric Apparatus,” Transactions
AIEE, 63 , 955-960 (December, 1944).

D. Ramandanoff and S. W. Glass, “Iligh-altitude Brush Problem,” Transactions
AIEE, 63 , 825-829 (November, 1944).

Howard M. Elsey, “Treatment of High-altitude Brushes,” Transactions AIEE
(August, 1945).

Fiq. 14-5.—Addition of auxiliary starting relay to circuit of Fig. 14-4.

Fig. 14-6. —Starting current of 1500-va motor-alternator, Signal Corps Type PE-218-D.

No load on alternator.

Sec. 14-5]

VOLTAGE REGULATORS

563

the normal full-load current. Such high starting currents cause: (1)
excessive brush wear, (2) voltage dip on aircraft electrical system,
(3) excessive load on contactor points unless an oversize contactor is used.
Extremely high currents may cause laminated brushes to explode.
Voltage dips on the electrical system can cause the release of vital relays
or contactors. To reduce the initial current surge a series resistor
(often an auxiliary series motor field) is added. When the motor is up to
speed, this resistor is shunted out by a contactor (see Fig. 14-4.) This
reduces the initial starting current, but the current again rises sharply if
the secondary contactor closes too soon. Clpsing of the secondary
contactor can be further delayed by an auxiliary starting relay con¬
nected as shown in Fig. 14-5. The curve of Fig. 14-6 indicates the
reduction in starting current effected by the use of the auxiliary starting
relay.

14-5. Voltage Regulators.—Since constant output voltage must be
maintained despite changes in load, shaft speed, and d-c input voltage,
some form of voltage-regulating device is used with an alternator. For
radar applications, an electronic voltage regulator is the most satisfactory
type. Although it weighs more than a simple mechanical regulator, an
electronic regulator should be employed on systems delivering 750 va
or more.

Electronic Voltage Regulators.— An electronic voltage regulator
consists of a voltage-sensitive element, an amplifier, and an output stage
that supplies d-c excitation for the generator or alternator field.

Three types of voltage-sensitive elements have been used in experi¬
mental regulators. One consisted of a VR-tube bridge excited from a
transformer and rectifier connected to the output of the alternator to be
controlled. A suitable filter could be added to the rectifier so that
regulation was performed with respect to the peak value of the output
waveform. Similarly, other types of filters could be used to regulate
with respect to the average value of output voltage, or to some chosen
value between peak and average. The filter introduces a time constant
that, in some cases, is too long to achieve the desired rate of response.

The second voltage-sensitive element, developed by Bell Telephone
Laboratories, was a bridge network made of thermistors and excited
from alternating current. This gives an a-c output error voltage that
can be readily amplified, but has the disadvantage of a relatively long
time constant. The thermistor bridge, though rather difficult to com¬
pensate for wide variations in temperature, regulates to the rms value of
the output wave, which is a considerable advantage for some applications.

The third form of voltage-sensitive element was a tungsten-filament
diode operated in the region of saturated emission. The filament was
heated by the alternator output through a transformer, and the anode

564

PRIME POWER SUPPLIES FOR RADAR

[Sec. 14-5

excited from the d-c power supply. The plate current varies in pro¬
portion to nearly the fourth power of the rms value of the alternator
output voltage. This provides a very sensitive signal voltage with a very
short time constant if the filament is of small diameter. Such a diode
must be ruggedly constructed in order to maintain the mechanical spacing
of the tube elements, and thus the tube characteristics, even under severe
mechanical vibration.

Fig. 14-7.—KS-15055 electronic voltage regulator designed by Bell Telephone Laboratories.

A conventional amplifier is used which must have sufficient gain to
provide the required over-all sensitivity. Stable operation of the
combination of voltage-sensitive element, amplifier, output stage, and
alternator demands that the usual conditions for stability of a servo
system be fulfilled.

Direct current excitation for the alternator field is provided by a
controlled rectifier fed from the alternator output. The controlled recti¬
fier may be a combination of transformer and rectifier controlled by a sat¬
urable reactor, or it may have grid-controlled thyratrons for rectification.

Sec. 14-5]

VOLTAGE REGULATORS

565

Bell Telephone Laboratories developed a regulated exciter, type
KS-15055, which weighed about 12 lb complete and was meant for use
with the PE-218 inverter. (See Fig. 14-7.) It regulated the 115-volt
output to about ±0.5 volt rms, but had a rather slow response and only
fair temperature compensation. The temperature compensation was
improved in a later model.

General Electric Company developed a similar regulator, type
3GVA10BY1, for use with PE-218-D inverters; it used a saturated-diode
voltage-sensitive element. (See Fig. 14-8.) This regulated the 115-volt
output to about ±0.1 volt rms and had good response and temperature
characteristics, but the diode was sensitive to vibration.

Fig. 14-8.—General Electric 1500-va aircraft inverter type PE-218-D, 115 volts, 400 cps,
and electronic voltage regulator.

In the latter part of 1944, more interest was shown in the development
of electronic regulators because of a trend toward the use of engine-
driven alternators that were too large for control by carbon-pile regulators
unless separate exciter generators were used. The ATSC Equipment
Division at Wright Field sponsored the development of two regulators
to control and excite engine-driven alternators rated 8 kva, 1-phase,
400 to 800 cps, 115 volts a-c. One developed by Bell Laboratories
weighed 33 lb; its operation was reported to be very satisfactory.

In 1945 Radiation Laboratory undertook the development of reg¬
ulators using a saturated-diode voltage-sensitive element and grid-
controlled thyratrons in the output. The intention was to perfect a
more or less universal regulator which could be applied to different
alternators by changing the thyratron output. The development had
progressed to the preliminary test model stage for two types; one type
for single-phase inverters which had been applied to the PU-7 2.5-kva
machine, and one type for 3-phase engine-driven alternators of 6.5- to
12-kva rating. The results were very promising, and it appears quite

566

PRIME POWER SUPPLIES FOR RADAR

[Sec. 14-5

certain that satisfactory electronic regulators can be developed for sta¬
tionary ground generating equipment as well as for airborne equipment.

Mechanical Voltage Regulators .—All mechanical voltage regulators are
prone to improper operation in the presence of vibration since they are
sensitive devices that balance a spring against a magnetic force. A
mechanical voltage regulator consists of two principal elements: (1) a
variable resistance in series with the generator field, and (2) a control
device, operating from the generator output voltage, which alters the

and adjusting Solenoid coil

screw

Fio. 14-9.—Cross section of carbon-pile voltage regulator.

variable resistance to maintain constant output voltage. The two
types of regulators commonly used in aircraft are the carbon-pile and
the finger types.

Carbon-pile Regulators .—The carbon-pile regulator (Fig. 14-9) was
first developed in England, where it is known as the Newton regulator
after the inventor. The variable resistance element consists of a stack
of carbon disks or annular rings placed in a ceramic or tempered-glass
cylinder. The cylinder is mounted in a metal housing which serves to
dissipate the heat from the pile and gives structural support. One end
of the pile rests against a button held in place by radial leaf springs;

Sec. 14-5]

VOLTAGE REGULATORS

567

the other end is retained by a screw usually referred to as the pile screw
or pile-adjusting screw.

The control element of the regulator is a solenoid coil and armature.
The current through the solenoid coil is proportional to the voltage to
be regulated, and the pull of its core on the armature is proportional to
the air gap between the two, and
to the coil current. The air gap
is adjustable by movement of
the core; this constitutes one of the
adjustments to be made on the
regulator.

With the core in fixed position
and the pile-adjusting screw tight,
the output voltage of the generator
will be high. As the pile screw is
loosened the voltage will drop, reach
a minimum point, rise, and then
drop again as shown in Fig. 1410.

The generator will regulate properly
to the left of the hump or to the right of the dip. Between these two
points, that is, on the downward slope of the curve, regulation will be
unstable. The slope of the curve to the left of the peak is less than
that to the right of the valley, giving better regulation. However, in
this region the carbon pile is under less pressure, and is thus more suscepti-

Fio. 14-11.—Output waveform showing amplitude modulation.

ble to mechanical vibration and shock. Most recent practice, therefore,
is to adjust the regulator to operate on the right-hand side of the dip.

When carbon-pile regulators were first used on inverters they were
mounted directly on the rotating machine. This gave rise to serious
troubles because of the susceptibility of the regulator to vibration.
Vibration of the carbon pile causes amplitude modulation or “jitter” of

Pile screw turns

Fig. 14-10. —Carbon-pile regulator ad¬
justment. Point A —bottom of dip—115
volts. Point B —optimum operating point
-—117 volts.

but also in increasing the interval between regulator adjustments, and
in reducing the wear of the carbon disks.

The carbon-pile regulator is affected by moisture. Moisture in the
carbon pile materially reduces the resistance, and frequently when a
motor-alternator is started after having stood for some time in an atmos¬
phere saturated with water vapor the output voltage is high—approxi¬
mately 135 to 145 volts. After the machine has run for an hour or
longer, the moisture is usually driven off and the voltage returns to
normal. During this drying-out period the carbon disks are often

the a-c voltage, which in a radar set shows up as spoking and blurring of
the indicator scope (see Fig. 1411). The frequency of the modulation
is normally 30 or 40 cps. The maximum “jitter” which can be tolerated
is approximately 1 to H volts.

The regulator should be shock-mounted as shown in Fig. 1412.
This procedure, together with adjustment of the regulator on the tight
side of the dip, helps not only in clearing up the troubles mentioned above,

Fig. 14-12.—Typical vibration mount for voltage regulator.

568

PRIME POWER SUPPLIES FOR RADAR [Sec. 14-5

Sec. 14-51

VOLTAGE REGULATORS

569

burned because, as the film of moisture is gradually reduced, it may
break down at one particular point on the face of the disk and the high
current-density at that point may be sufficient to burn the disk. In
this event, the regulator pile must be removed and the damaged disk
replaced.

One fundamental defect of the carbon-pile regulator is the lack of any
means for insuring uniform voltage distribution across the stack. Some
carbon junctions may be tightly
mated, with low voltage drop;
others may be loose, with high
voltage drop. If the drop per
junction exceeds 1 to 2 volts,
sparking may occur which will
ruin the pile.

Under changing load condi¬
tions, the regulator -acts to in¬
crease or reduce the field current;
as in any action of this kind, hunting may result. In order to reduce
hunting, a stabilizing transformer (Fig. 14-13) is now used with most of
the larger alternators. Such a transformer provides a correction depend¬
ing on the rate of change of excitation.

The resistance of the carbon pile ranges from 2 to 60 ohms. 1 Its
electrical rating is based on the rate of allowable heat dissipation, and is
given in watts. The unit often used on aircraft inverters is rated at
35 watts. Smaller inverters, notably the Eclipse 100- and 250-va units,
use a smaller regulator rated at 20 watts, while 2500-va inverters use a
75-watt regulator, of the same physical size as the 35-watt unit, but
with fins to increase the rate of heat dissipation. For the purpose of
using a smaller regulator than would otherwise be possible, the carbon
pile can be shunted with a fixed resistor. Such an arrangement increases
the range of resistance over which the carbon pile -must operate, and care
must be taken that the maximum stable range of the pile is not exceeded. 2

The coil of the carbon-pile regulator usually used in aircraft inverters
has a resistance of 185 ohms and a d-c rating of 115 to 125 ma, which
gives a voltage drop of 21 to 23 volts. As the voltage to be regulated is
115 volts alternating current, rectification and voltage-dropping are
necessary. Rectification is provided by a selenium dry-disk rectifier,
in series with a “globar” resistor which provides some temperature

1 Although the 35-watt earbon-pile regulator can be made to operate over a range
of resistance from 2 to 60 ohms, it has been found desirable to use only the range from

2 to 30 ohms since the high-resistance end of the range has a tendency to be unstable.

2 W. G. Neild, “ Carbon-pile Regulators for Aircraft.” AIEE Transactions, 63,
839-842 (November. 1944).

+ d-c

Carbon-pile

voltage

regulator

Alternator

field

Fig. 14-13.—Schematic diagram of
stabilizing transformer in voltage regulator
circuit of 400-cps aircraft inverter.

570

PRIME POWER SUPPLIES FOR RADAR

[Sec. 14-5

compensation. The voltage is reduced either by a small auto-trans¬
former or by a dropping resistor. 1 In any case, a variable resistor is
used, either on the a-c or d-c side of the rectifier, to provide a voltage
adjustment whose range is approximately 10 volts.

Figure 14T4 shows a carbon-pile regulator for use with a 10-kva,
3-phase, 208-volt engine-driven generator; Fig. 1415 is a schematic
diagram of the circuit. Note the two potential transformers, connected
in open delta, which energize the regulating coil, so that the regulated

Fig. 14*14.—General Electric Company voltage regulator for 10-kva alternator.

voltage is an average of the three line-to-line voltages. Note also the
antihunt circuit and coils on the solenoid.

It is probable that further development of the carbon-pile regulator
can greatly extend the usefulness of the device. At the close of World
War II, Leland Electric Company, of Dayton, Ohio, had developed
experimental models of improved carbon-pile regulators that appeared
to have a greatly extended operating range of resistance and improved
resistance to humidity as compared to earlier service models.

Finger-type Regulators.— Finger-type voltage regulators are similar
in operation to the carbon-pile type, except that the resistance is varied
in fixed steps rather than being continuously variable between minimum
and maximum resistance. Mechanical construction varies widely with

1 A third method, employed on the 1500-va series PE-218 inverters as well as a
number of others, is the use of a low-voltage tap on the armature winding.

Sec. 14-6]

SPEED REGULATORS

571

different manufacturers. In general, a voltage-sensitive element, con¬
sisting of a solenoid coil and a movable armature, is connected to a
multiple contactor. Movement of the armature from the closed to the
open position progressively short-circuits steps of resistance connected
to the contacts. It is necessary to choose the resistance steps with the
field-excitation characteristic of the alternator in mind, so that each
progressive step of resistance produces an approximately equal change
of output voltage. The incremental change in output voltage produced
by one step of resistance determines the limit of sensitivity of the regu¬
lator. An air dashpot is usually provided to damp any oscillation or
hunting of the armature.

Fig. 14-15. —Schematic diagram of a General Electric voltage regulator Type GEA-2-B2
and 3-phase 230-volt alternator with exciter.

In field service, the usefulness of the finger-type regulators was
limited by the tendency of the contacts to stick and burn, and by corro¬
sion of the contacts due to moisture and salt air. In addition, the device
is very difficult to repair in the field. Consequently, finger-type regu¬
lators have been used on radar systems only rarely.

14-6. Speed Regulators. —The a-c frequency generated by motor-
alternator sets varies over a wide range with changes in input voltage,
load, altitude, and temperature. At high altitude, low temperatures and
air densities are encountered. The low temperature tends to lower the
speed by reducing the resistance of the motor field circuit, whereas low
air density allows the speed to increase because of lower windage losses.
The following test data indicate the conditions for maximum and mini¬
mum frequency of the 1500-va PE-218-C and PE-218-D inverters.

572

PRIME POWER SUPPLIES FOR RADAR

[Sec. 14-6

Maximum frequency at 28.5 volts, i load, 35,000 ft, —15°C,

Leland PE-218-C 485 cps

GE PE-218-D 458 cps

Minimum frequency at 28.5 volts, full load, sea level, —35°C,

Leland PE-218-C 401 cps

GE PE-218-D 392 cps

The variation in frequency caused by change in input voltage and in
temperature is indicated in the following table.

Table 14-4.—Changes in Frequency of Inverters with Temperature and

Voltage

Frequency, cps

Input

Temperature,

voltage

°c

Leland

GE Co.

PE-218-G

PE-218-D

-45

373

379

+25

396

+55

406

398

-45

411

404

+25

443

423

+55

449

428

Over-all regulation

Leland

PE-218-C

GE Co.
PE-218-D

In cps

In per cent

17.0

11.5

All data were taken at sea level and with full rated load on inverter.
The GE PE-218-D unit has a compensating resistor in series with the
field which accounts for its slightly better regulation. It also has an
adjustable resistor which allows the frequency to be varied over a range
of approximately 40 cps. These inverters are shown in Figs. 14T6
and 14T7.

In most radar applications, such a range in frequency is not objection¬
able. Certain indicator and computing circuits, however, require much
closer regulation of the order of + 2j per cent. Good speed regulation
also considerably reduces the problem of voltage regulation. In accord¬
ance with the need for better speed characteristics of inverters, the latest
Army-Navy specifications (AN-I-10) stipulate the following frequency
limits: For all voltages between 26 and 29 volts and at any load from
& to full, the allowed frequency limits for a temperature range of — 10°C

574

PRIME POWER SUPPLIES FOR RADAR

[Sec. 14-6

to + 10°C shall be 390 to 410 cps; over the same range of voltage and
load, the frequency limits for a temperature range of — 55°C to +70°C
shall be 380 to 420 cps.

Table 14-5 gives the frequency range of inverters now in general use,
and in the column headed “Remarks’’ the motor type or method of
speed control is indicated. All data refer to a temperature of 25°C and
sea-level pressure.

Table 14-5. —Speed Control of Certain Motor-alternator Sets

Rating
va phases

Frequency, cps

Manufacturer

Style

26 volts
full load

29 volts
i load

Remarks

Eclipse.

100 30

12123-l-A

410

Lee Regulator

Eclipse.

250 30

12121-1-A

400

410

Lee Regulator

Leland.

500 10

10596

395

475

Compound-wound

Wincharger .

750 10

PU-16

390

403

Carbon-pile regu¬
lator

Holtzer-Cabot.

1000 30

MG-153

340

395

Resonant

Leland.

1500 10

PE-218-C

395

450

Shunt-wound

GE.

1500 10

PE-21S-D

395

440

Shunt-wound

Airways.

2500 ltf>

PU-7

410

430

Regulating field

Eclipse*.

840 10

800-1-C

730

900

Compound-wound

* Nominal rated frequency 800 cps.

Lee Regulator .—The Lee speed regulator is a centrifugal device which
alternately opens and closes a short circuit across a fixed resistor in
series with the motor field. The short-circuiting contacts are on the
centrifugal device and can be set to open and close at any predetermined
speeds within 5 per cent of each other. Speed regulation is therefore
good; it can be maintained at approximately 5 per cent. This type of
regulator creates a good deal of r-f noise that is difficult to suppress, and
gives pronounced modulation of the output voltage.

Voltage Regulator Control .—Speed regulation can also be provided
by means of a regulating field controlled by the generator voltage regu¬
lator. This method is used in the 2500-va Type PU-7 inverter designed
by Wincharger and built by Wincharger and Airways. It is shown
schematically in Fig 14T8.

As the input voltage or inverter load changes, the resistance of the
carbon pile in the voltage regulator varies to maintain constant output
voltage. This also serves to vary the current through the motor regu¬
lator field in the proper sense to maintain constant speed. The motor is
designed to obtain proper division of flux between the main field and
the regulating field. The resistances of the regulating field and of the

Sec. 14-6]

SPEED REGULATORS

575

Fia. 14-18.—Schematic wiring diagram of PU-7 aircraft motor-alternator, 2500 va, 115 volta,

400 cps.

Fig. 14-19.—Schematic circuit of Holtzer-Cabot MG-153 aircraft motor-alternator.
Output ratings: 750 va, 115 volts, 400 cps, 3-phase; 250 va, 26 volts, 400 cps, 1-phase.
Ground terminal common to all circuits.

576

PRIME POWER SUPPLIES FOR RADAR

[Sec. 14-6

alternator field must be kept in proper relation to the normal range of

resistance of the carbon pile in order to obtain good speed regulation.

n r-Bushing

[l / /^—Insulating

\\ I J spacers

Fig. 14-20.—Holtzer-Cabot Electric Company carbon-pile speed governor.

If the regulator is removed from the circuit, the alternator will still
generate a voltage because the field current will flow through the motor¬
regulating field to the generator field. In the case of inverters not

Fig. 14-21.—Wincharger Corporation aircraft

Sec. 14 6 ] SPEED REGULATORS 577

having the regulating field, removal of the regulator from the circuit
kills the alternator voltage.

In order to get good results by this method, the motor field must
operate below saturation; this adds weight to the magnetic circuit.

Tuned Circuit Control.-^An interesting method of speed control has
been used by the Holtzer-Cabot Electric Company in their MG-153
inverter, Fig. 14-19. The reactor and condenser connected in series
with the rectifier which energizes the regulating field are designed to
resonate at a frequency well above the rated frequency of the alternator
(in this case, 400 cps). The circuit therefore operates on the low-
frequency side of the resonance curve; any change in speed will alter the
reactance of the circuit and thus vary the field current in the correct
direction to provide speed regulation. Should the motor attain a speed

motor-alternator with Holtzer-Cabot speed control.

578

PRIME POWER SUPPLIES FOR RADAR

[Sec. 14-6

that would generate a frequency above resonance, the machine speed
would continue to increase, being limited only by friction and windage
losses.

Centrifugal Control .—The most recent method of speed regulation
to be used on aircraft inverters is a carbon-pile governor as used by
the Holtzer-Cabot Electric Company. It is shown in Fig. 14-20 and also
in Fig. 14-21 mounted on a 750-va PU-16 inverter. The electrical
connections are shown in the schematic diagram Fig. 14-22. A centrif¬
ugal device on the end of the inverter shaft acts against the carbon pile
in such a manner that increased speed will reduce the pressure on the
carbon pile and reduced speed will increase the pressure. As shown in
Fig. 14-20, when the machine is at rest the carbon pile is held in compres-

Alternator field

Fio. 14*22.—Schematic diagram of Wincharger PU-16 aircraft inverter, 750 va, 115 volts,

400 cps.

sion by the large coil spring in the rotating element. The resistance
is then least, giving maximum field for good starting characteristics. As
the machine speed increases, the centrifugal weights compress the spring
and reduce the pressure on the pile, increasing its resistance. Should
the machine exceed its rated speed, the carbon pile will be compressed by
the spring under the adjusting screw. At rated speed, the carbon pile
is balanced between these two springs and a slight change in speed will
cause a relatively large change in resistance. Springs A and B position
the tube holding the carbon pile. 1

Electronic Speed Controls .—The Eclipse-Pioneer Division of Bendix
Aviation has recently developed an electronic speed control for use on
motor alternator sets of 1500-va capacity and larger. This regulator is
designed to hold speed within the limits of Army-Navy Specification
AN-I-10.

1 C. T. Button, “A Carbon-pile Speed Governor,” A1EE Transactions, 66, 4
(January 1946).

Sec. 14-7]

DYNAMOTORS

579

Fig. 14-23.—Eicor Inc. aircraft dynamotor.

to give voltages as high as 2000 volts, but such machines meet severe
difficulties with commutation and insulation. Dual- and triple-output
dynamotors are very common, and several machines having four outputs
(Fig. 14-23) have been built, but it is impractical to go beyond this
because of the large number of windings and commutators involved.

Dynamotors for military aircraft are built for an input voltage of
27.5 volts. For automobiles, commercial aircraft, and miscellaneous
use, dynamotors are built for input voltages of 6, 12, 32, and 110 volts.
Output ratings vary from 14 or less to over 1200 volts, and from 30 ma
to 5 amp, with any combination of two, three, or four at a time. Weights
vary from 5 lb, for a total output of 20 watts, to 26 lb, for an output of 400
watts. Efficiencies range from 40 per cent to 60 per cent.

The dynamotor suffers from poor regulation. Furthermore, varia¬
tions in input voltage may be as great as 10 per cent. The dynamotor

14-7. Dynamotors. —To supply smaller radar sets with moderate
power at not over 1000 or 1200 volts, a dynamotor is often more econom¬
ical in weight and efficiency than an inverter. A dynamotor has con¬
ventional d-c shunt- and series-field windings on the stator and one or
more armature windings on the rotor. The rotor winding is excited
through brushes and a commutator from the input voltage.

A single rotor winding can be tapped to give the required secondary
voltage. Alternatively, separate rotor windings can be used, with
turns-ratios to the primary winding chosen to provide the correct output
voltages. The required d-c voltages are brought out through com¬
mutators from the secondary windings. Dynamotors have been built

580

PRIME POWER SUPPLIES FOR RADAR

[Sec. 14-7

can be designed for an input of 19 or 20 volts if it is to be used with an
actual line voltage of 27.5, and a variable control resistor put in series with
the line. This resistor can be a carbon-pile voltage regulator, with the
carbon pile in series with the line and the operating coil across the line

Fig. 14-24.—Bendix dynamotor.

Carbon-pile

voltage

regulator

Demagnetizing
field \

Voltage

adjusting

rheostat

Regulating

.field

o-r Low-voltage
output

+ High-voltage
output

Motor l-oi-g
commutator

1 I - —r—[N _

Commutators

41 Ml 4)

5™ gats §fc

.9? | « —

I Booster I
1 armature I

H— 1 -c |_I_I_ pop i_I_I TThis represents

I_I I_/TTr;__J connection from

_I—--— g - -i i-— —-i armature wind-

TO wfl 1 Reeu- S d ln S s to commu-

I g I tator bars

wP^j I field E w C ! -High-voltage

Input O-UP- M-\ -—___Nj i oulput

output

Fia. 14-25.—Schematic diagram of dual-output dynamotor with booster windings and

regulating field.

just ahead of the dynamotor. For an input from 25 to 29 volts at
constant load, the regulation of the output voltage can be held within a
range of 5 to 10 per cent. Regulation becomes poorer with changing load.

Booster Armature Voltage Regulation :—A recent development to
improve dynamotor regulation is the construction in the dynamotor

Sec. 14-8]

VIBRATOR POWER SUPPLIES

581

itself of a booster armature winding and regulating field. A three-voltage
dynamotor is shown in the photograph of Fig. 14-24 and the circuit of a
dual-voltage machine is shown schematically in Fig. 14-25. In any
multi-output dynamotor only one voltage can be regulated, but, except
in the event of very unevenly loaded circuits, the unregulated voltages
will closely follow the regulated voltage. Regulation can be handled in
several ways: (1) all output circuits have windings on the booster arma¬
ture although only one of them is controlled (Fig. 14-25); (2) only the
voltage to be regulated has a booster winding; and (3) the voltage to be
regulated is generated entirely in the windings of the booster armature.
The third method is practical only for low voltages, because of the large
number of turns and relatively high field current required to generate a
high voltage. 1

Over ranges of input voltage from 25 to 29 volts, from no load to
full load on the dynamotor, the output-voltage change will be approxi¬
mately 3 per cent. The booster armature and regulating field increase
the size and weight of the dynamotor, but the regulator itself can be
considerably smaller than a series regulator because it carries only the
field current rather than the line current.

14-8. Vibrator Power Supplies. —If relatively small amounts of power
are required, vibrator power supplies are useful. Conventional vibrators,
such as those used commercially in automobile radios, are capable of
supplying 50 to 60 watts of square-wave alternating current to a trans¬
former. The transformer output may be rectified-and filtered to furnish
direct current of appropriate voltage.

Vibrator power supplies can, unlike dynamotors, supply a number of
different d-c output voltages without disproportionate increase in the
weight of the power supply. For example, it is possible to supply 2500
volts direct current at 5 ma, 250 volts direct current at 100 ma, and — 150
volts direct current at 5 ma, at approximately the same total weight as
that required for conventional power supplies designed to run from
115-volt 60-cps a-c lines. The vibrator power supply just described
weighs from 6 to 8 lb, depending on how it is packaged and on the degree
of filtering required.

The output voltage of a vibrator power supply can be regulated by
use of the series-tube type of electronic regulator, which is apt to be
wasteful of power. Further, output power is consumed by the rectifier-
tube cathodes. Where a number of d-c output voltages are required,

1 In any case, it is seldom practical to regulate the highest-voltage output since
current-limiting resistors are required in the regulator coil circuit, and at high voltages
the loss in them is excessive. It is also less important to regulate the higher voltages,
for this can readily be done by regulating circuits in the radar set itself.

582 PRIME POWER SUPPLIES FOR RADAR [Sec. 14-9

rectifier cathodes may use up a large part of the 50 to 60 watts of avail¬
able power.

Two or more vibrator power supplies can be designed for operation in
series or in parallel on the d-c output side, so that larger currents or
voltages can be obtained from small vibrators. Large vibrators, capable
of supplying 200 watts or more from 12- to 14-volt or 24- to 28-volt d-c
supplies, are available, but it is usually more, convenient to use conven¬
tional inverters with transformer-rectifier power supplies for outputs
greater than 250 watts.

Vibrator power supplies usually give efficiencies of 50 to 70 per cent,
based on d-c output vs. d-c input.

Precautions must usually be taken to reduce radio interference from
vibrator power supplies. Small r-f chokes in the power input leads, mica
r-f bypass condensers on input and output, and careful shielding and
grounding usually provide adequate radio interference suppression for
aircraft use. Where extremely low noise level is required it may be
necessary to shield the vibrator, transformer, and each d-c ripple filter
separately, and use r-f chokes in each transformer connection. How¬
ever, it is usually less troublesome to suppress radio noise in a vibrator
supply than in a small dynamotor.

Vibrators can be obtained in hermetically sealed containers, making it
possible to design power supplies for operation under extreme conditions
of altitude and humidity.

Production-type small vibrators are available with reed frequencies
from about 100 to 115 cps. These vibrators have a useful life of at least
500 hours when used with well-designed power supplies.

Vibrators have recently been developed with reed frequencies of about
180 cps. Smaller transformers can be used at this higher frequency, so
than an over-all weight reduction of 20 to 25 per cent may be achieved.
The life of such vibrators may be somewhat less than that of low-fre¬
quency vibrators. A more complete treatment of vibrator power sup¬
plies is given in Vol. 17, Chap. 12 of the series.

14-9. Summary of Recommendations for Aircraft Radar Power.

1. Consider the radar-radio power-supply problem of a specific air¬
craft as a whole. What dynamotor can be eliminated? What
inverters can be combined? Is all equipment uniformly designed
to operate from one standard a-c source? Often enough weight
can be saved to justify such refinements as an electronic voltage
regulator.

2. Use a direct-driven generator whenever possible, either at constant
frequency (if airplane is so equipped) or at variable frequency. If

Sec. 1410]

FIXED LOCATIONS

583

portions of the installation require fixed frequency, consider an
auxiliary d-c to a-c motor-alternator.

3. Use electronic voltage regulation for engine generators or motor
alternators.

4. Consider vibrators for small loads.

GROUND AND SHIPBOARD SYSTEMS

Power for ground radar systems should be obtained from commercial
electric service whenever possible, with certain precautions outlined
below. The general problem of power supply for ground radar falls into
four main groupings:

1. Fixed locations with commercial electric service available.

2. Large systems (with requirements for highly dependable service
under all conditions) at fixed locations without commercial electric
service, or for mobile use.

3. Small systems for use in fixed locations without commercial power,
or for mobile use.

4. Small ultraportable mobile sets.

In selecting a specific engine-generator set, or any specific alternator,
serious consideration must be given to the specifications of the set (the
alternator in particular) if satisfactory performance and characteristics
are to be obtained. One good tabulation of standard Army power sup¬
plies is Signal Corps Manual TM 11-223. However, most of the sets
listed therein were not originally designed with radar in mind. Accord¬
ingly, their electrical performance may not meet radar needs without
modification. A fuller discussion of the factors involved in choosing
alternators and engine-generator sets is given in Vol. 17, Chap. 12, Radi¬
ation Laboratory Series.

14-10. Fixed Locations. —Commercial power supply for radar installa¬
tions must be provided with three major considerations in mind: (1) reli¬
ability required, (2) voltage stability of supply, (3) interference from
common loads.

Reliability .—If extremely reliable service must be provided, com¬
mercial service from a first-grade public utility is most satisfactory, pro¬
vided that it is backed up by emergency feeders duplicating normal
service (preferably by an alternate route) to a network station of the
public-utility system. An emergency engine-alternator set (which may
be made automatic-starting if deemed necessary) should also be provided.
This arrangement is preferable to constant reliance on local generation.
A regular maintenance schedule must be followed, with the emergency
engine operated for a minimum of one hour per week at no load and a

584 PRIME POWER SUPPLIES FOR RADAR [Sec. 1411

minimum of two hours per month at full load. For such emergency
service as that outlined, gasoline-powered prime movers are reliable and
satisfactory.

Voltage Stability of Supply .—If the service is obtained from a source
unstable in voltage, local voltage stabilization must be employed. If the
voltage changes take place slowly, without transients, they can be elimi¬
nated by means of induction regulators, with automatic or manual con¬
trol; tapped autotransformers, manual or servo-driven; or (for small
loads) variacs. For example, consider the use of commercial power by a
remote beacon station served by a line shared with other power users.
As night falls, increasing load on the line lowers the voltage at the beacon.
Servo-driven variacs have proved useful in such a situation.

Interference from Common Loads .—If the loads sharing power service
with the radar impose high intermittent demands, and especially if the
total capacity of the system is low with respect to these loads, serious
transient interference may be encountered. An isolating motor-gener¬
ator is the only satisfactory solution for such difficulties. If synchronous
frequency is not essential, induction-motor drive is preferable to the
greater complexity of a synchronous motor. It is good practice, where
possible, to make input and output services identical, and to provide
means for bypassing the isolating set in case of trouble. That is, if the
main service is 220 volts, 3-phase, 60 cycles, the motor-generator set
should be 220-volt 3-phase input (60 cycles) to 220-volt 3-phase output
(58 cycles).

14-11. Large Systems Where No Commercial Power Is Available.—

Where 24-hour operation of a prime mover is required, it is necessary to
provide duplicate power generation equipment, regular and emergency.
Such equipment should be interchangeable, and the two sets should be
used alternately to ensure reliable service. Where extreme reliability is
desired, three engines should be furnished; one can then be disassembled
for maintenance without risking complete system breakdown if the service
engine fails. Generators of a size at least twice the estimated load should
always be provided, to permit future additions of auxiliary devices not
initially specified. Diesel engines are definitely more reliable for con¬
tinuous operation than gasoline engines. Diesel fuel and diesel exhaust
fumes are less hazardous.

Electric power for loads larger than 7.5 kva should be 208/120-volt
3-phase 60-cycle alternating current. It is desirable to use 3-phase
60-cycle because electric motors of this rating are compact and simple to
operate. Weight savings in rectifier-filter supplies can usually be achieved
with 3-phase power, if this is important.

For large mobile systems it is well to investigate availability of stan¬
dard U.S. Army power-supply units. Unfortunately, the voltage

Sec. 1413]

ULTRAPORTABLE UNITS

585

regulators in such systems are almost uniformly unsatisfactory for radar
equipment since they have a tendency to produce modulation in the
amplitude of the a-c voltage. It is often necessary to resort to hand
rheostat control of the exciter field or the alternator field. Radar loads
are usually constant or nearly so, and hand control requires only occa¬
sional adjustment after,the equipment has come to normal operating
temperature. The engines are usually provided with flyball-type speed
governors which are satisfactory when well maintained, and keep the
output frequency within a range of about 58 to 62 cps.

14*12. Smaller Mobile Units. —-If high reliability is required, the same
considerations must be observed in this case as in the case of large
systems, notwithstanding the weight penalty. For example, a navigation
aid required to operate 24 hours per day under all conditions must use
conservative, long-lived prime movers and be provided with standby
equipment, though it may consume only 750 watts.

Much design effort has been expended on packaging units of about
500-lb weight and 5-kw output in a readily portable form. There has
also been much development of two-cycle gasoline engines for power
units up to about 2-kw output. It is likely that two-cycle engines coupled
to 400-cps generators will be available in the future in many ratings;
these units are much lighter and more compact than four-cycle engines
with 60-cps generators of equivalent rating.

It is true that two-cycle engines have some disadvantages. They
are often more difficult to start than the small four-cycle engines, and,
because of their tendency to foul exhaust ports and spark plugs, they are
likely to require more maintenance. However, as mobile units, they have
two advantages over and above their lightness of weight and their
compactness. They are easier to repair in the field and require less
replacement of parts than the four-cycle engines, which are subject to
valve-fouling and burning.

14*13. Ultraportable Units .—Where extremely light weight is required
this can be obtained only by sacrificing reliability or by shortening the
required period of operation.

Ultraportable ground radar systems usually need very little power.
Where only a few hours of operation are required, the systems can be
powered by small storage batteries which operate vibrator power supplies
or dynamotors.

Where longer operation is required, very small two-cycle engines con¬
nected to permanent-magnet-field 400-cps generators have been developed
by the Jacobsen Manufacturing Company, Racine, Wis., and the Judson
Manufacturing Company, Philadelphia, Pa.

Jacobsen produces a unit rated 125 watts 400 cps weighing about
13 lb. A single-cylinder, air-cooled, two-cycle engine is direct-connected

586 PRIME POWER SUPPLIES FOR RADAR [Sec. 1414

to a permanent-magnet generator. The speed is controlled by an
air-vane governor.

Judson produces several small models, one of which is rated 150 watts
400 cps and weighs about 15 lb. The general design is similar to that of
the Jacobsen machine, except that the engine is belt-connected to the
generator.

There is no way of regulating the output voltage of permanent-magnet
generators, but capacity in series with the output will hold the output
voltage constant to about ±5 per cent despite changing load. The
voltage can be altered to compensate for temperature changes by manual
adjustment of the speed governor on the engine.

Work has been initiated on the development of small prime movers
other than conventional gasoline engines. Small steam engines that
were capable of about 300 mechanical watts output were built by Radia¬
tion Laboratory, but no satisfactory boiler had been developed at the
close of activity. Small steam engines and gas turbines are attractive
because of their ease of control and flexibility. Further development
would probably produce some worth-while small prime movers.

14-14. Ship Radar Systems. —The problem of providing power for
large shipborne radar systems is principally that of stability. Most
modern warships have 440-volt, 3-phase, 60-cps power supply which is
subject to transient fluctuations of 10 to 20 per cent in voltage and per¬
haps 5 per cent in frequency. Transients are caused by the sudden
application of large loads such as gun turret drives and airplane elevators.

Good results have been obtained by powering the radar system from a
60-cycle motor-generator set. An induction motor is used to drive the
alternator; when not heavily loaded, the motor shows a relatively small
change in speed for a change in input voltage. Motor speed tends
to follow a change in frequency, but the mechanical inertia of the set is
usually adequate to hold up the speed during the usual short-period
frequency transients. The induction motor rating should be about
50 per cent larger than that required to drive the alternator. It is
desirable to have the alternator output the same as the ship’s power so
that the radar system can be operated directly from the ship’s supply in
case of breakdown or maintenance shutdown of the motor-alternator set.

The motor may be direct-coupled or belt-connected to the alternator;
usually direct coupling is preferred because of its simplicity. The output
frequency of a direct-connected alternator will be less than 60 cps by the
slip of the induction motor. This results in an output frequency of
57 to 58 cps, which is normally satisfactory for the operation of trans¬
formers or other 60-cycle equipment.

There is no really satisfactory means now available for regulating the
output voltage of the alternator. Most of the available voltage regu-

Sec. 14-14]

SHIP RADAR SYSTEMS

587

lators have a tendency to be unstable, exhibiting rapid hunting of about
20 to 40 cps. This may not be troublesome on lighting or motor loads,
but it is one of the major causes of spoking of PPI displays and instability
of other forms of radar presentation.

One method of using regulators has been followed with some degree
of success. That is to provide a rheostat in series with the regulating
resistance of the regulator in the field circuit. Assuming that 115-volt
output is desired, the regulator can be adjusted to regulate at 118 to 120
volts and enough resistance cut in, by means of the rheostat, so that
the voltage is 115 volts at full radar load with everything at normal
operating temperature. Under normal operating conditions, then, the
regulator is all out and not functioning. If the voltage should rise, as
during warmup period or when the radar is on stand-by, the regulator
will cut in when the voltage comes up to 118 to 120 volts and prevent
further rise in voltage. If there is a load greater than normal causing the
output voltage to drop, the manual rheostat will have to be adjusted.
However, with the motor-generator set acting as an electromechanical
flywheel to take up transient fluctuations in the ship’s power supply,
operation is reasonably steady and satisfactory.

CHAPTER 15

EXAMPLES OF RADAR SYSTEM DESIGN

By R. G. Herb and R. L. Sinsheimer

16-1. Introduction. —The development of a new radar system may be
called for because of recognition of a new application for which radar has
not been used but for which its successful use appears possible. In
other cases, a development may be justified for an application where radar
is in successful use but where improved results could be expected by the
use of more modern equipment.

Early ideas on a new system and initial proposals may come from a
development laboratory or from the potential users of the equipment.
Before design characteristics can be successfully crystallized, regardless
of the origin of a proposal, there must be an extensive interplay of ideas
and of information between specialists in the following categories: (1)
application specialists representing the potential using organization, who
must contribute necessary information on desirable performance char¬
acteristics, limitations on size, weight, and power consumption, and
limitations on the number and skill of operators and maintenance men;
(2) component specialists, who must contribute information on the status
of development and on the limitations of the many component parts that
make up a complete system; (3) system specialists with experience in the
design and operation of radar systems.

Normally a man experienced in system design is best able to coordinate
the over-all development project. He must have a supporting group of
experienced systems men to assist on the design problem and to carry out
operational test work that may be desirable, and he must have the con¬
tinued advice and support of specialists of the first two categories listed
above.

Versatility .—Initial planning for a radar system may be made with
one specific application in mind. As plans progress, possibilities of
related applications are generally recognized and consideration is given
to including facilities that improve the system in versatility. The value
of versatility has been amply demonstrated, not only for meeting related
applications but for meeting changing conditions frequently encountered
in the central application.

Provision for versatility, unless ingeniously made, may cost heavily
in increased complexity, size, or weight ; further, the utility of the set for

588

Sec. 151]

INTRODUCTION

589

the principal application may suffer. How far to go with such provisions
and how best to include them are problems that frequently outweigh in
importance any other design problem. No rules can be given for guid¬
ance along these lines, but the degree of success to be expected will depend
markedly on the extent to which development specialists are familiar
with problems of operation in the using organization and on the degree to
which representatives of the using organizations have become familiar
with the technical problems, the possibilities, and the limitations of radar.

Requirements for Component Development .—With sufficient care in
design and a sufficiently conservative policy, a radar set might be designed
making use of only those components on which development work has
been completed. Ordinarily the improvement to be gained in system
performance or in general utility by improvement in certain components is
sufficient to warrant component development work. The extent to
which such requirements can safely be included must be determined from
consideration of the time schedule to be met and from a careful, realistic
appraisal of the development time needed. Sound system-design work,
together with performance tests, can serve in a valuable way to direct
component-development work along the most advantageous lines.

Detailed Problems in Design .—General rules for guidance on the many
detailed problems encountered in the development of a radar system
would be extremely difficult to formulate because of the multiplicity of
applications with radically differing requirements. Information accu¬
mulated through experience on a large number of systems can be pre¬
sented most easily by outlining the development of successful systems
from the early-idea stage on through to their operational use.

Two typical system developments are described in this chapter:
(1) a high-performance ground-based set for air surveillance and control;
and (2) the AN/APS-10, a lightweight airborne set for air navigation.
Considerations leading to the selection of these systems are as follows:

1. Substantial development and design effort went into both systems
and important advances resulted.

2. Both systems are relatively simple, and design problems encoun¬
tered in their development are more basic in nature and more
generally applicable than in the case of a more elaborate system,
where usually a large proportion of the system is very specialized
in nature.

3. These two systems represent opposite extremes in requirements.
Limitations on factors such as size, weight, and power requirements
for the ground-based set were largely subordinated to the require¬
ment for the best possible radar performance. In the case of the
airborne set, severe limits were imposed on weight, size, and similar

590

EXAMPLES OF RADAR SYSTEM DESIGN

[Sec. 15-2

factors, and the ingenuity of the development and design men was
taxed to meet the minimum acceptable radar performance within
these limits.

A detailed treatment of further systems beyond these two would be
of questionable value, since changing requirements may soon make
obsolete all but the more general, basic developments of the past. Radi¬
cally new requirements will be met only by radically new developments,
and to be firmly bound by past experience would stifle progress. Ingen¬
ious technical men with good facilities, free in their thinking, working in
close touch with using organizations, fully informed on operational
problems and planning—these are the important requirements for future
advances.

16-2. The Need for System Testing. 1 —One general remark concerning
system design is sufficiently important to be made before taking up the
design examples. No radar system is complete until adequate provisions
for performance testing and maintenance have been made and appropriate
maintenance procedures prescribed.

The most important function of test equipment in radar maintenance
is to permit quantitative measurement of those properties of the system
which affect its range performance. Experience has shown that it is
essential to determine by reliable quantitative methods how well a radar is
operating. Under most circumstances, the important units of test
equipment should be built into the radar in a way that permits their most
convenient use. If limitations of weight and bulk do not permit the use
of built-in test equipment, suitable test points should be provided to
permit convenient and adequate tests to be performed frequently on the
important parts of the system.

Radar Performance Figure .—The ratio of P, the pulse power of the
radar transmitter, to <S m m, the power of the minimum detectable signal,
is a measure of the radar performance. This is the fundamental quantity
studied in tests. The radar equation given as Eq. (2-46),

shows that all factors except P and (S min are either invariable or beyond
our control once the radar has been designed.

A quantity closely related to Smin is usually measured rather than
S m in itself. This may be the power of the weakest test signal that can be
detected, or of a test signal that produces some other easily reproducible
effect. Because of the effects of presentation time and pulse width

• By R. D. O’Neal and J. M. Wolf.

Sec. 15-2]

NEED FOR SYSTEM TESTING

591

(Secs. 210 and 211), such test signals are generally not equal to but
differ from it by a constant ratio. The ratio between pulse power and the
power of such a test signal, P/St, expressed in decibels, is called the
“radar performance figure” and is a suitable measure of the ability of
the system to see radar targets.

Figure 15T shows the range performance on various types of radar
targets as a function of the radar performance figure. As explained in
Chap. 2, radar range performance does not always follow the fourth-power
law of Eq. (1), but the performance
figure remains of vital importance in
determining what fraction of the
maximum radar range can be realized
by a given system against a given
type of target, regardless of the
existing propagation conditions.

The Inadequacy of Guessing Per¬
formance .—It has often been wrongly
assumed that over-all radar perform¬
ance can be adequately judged with¬
out using test equipment by means
of one of the following “rule-of-
thumb” criteria: (1) the general
appearance of the picture seen on
the radar indicator, (2) the maxi¬
mum range at which target signals can be seen, or (3) the signal st rength
above noise of the echo from a “standard” target.

Both (1) and (2) are strongly affected by changes in propagation
conditions 1 as well as by interference effects resulting from composite
targets, 2 tidal changes, 3 etc. Although the effect of anomalous propaga¬
tion can be practically eliminated by choosing a near-by weak target
signal as a standard, such a favorable choice of “standard target” does not
necessarily eliminate interference effects. Targets that do not show such
effects in some degree are exceedingly rare.

These rule-of-thumb criteria are inadequate for the consistent judg¬
ment of radar performance, as has been shown by surveys of radar
performance made on radar equipment in the field during the war.
Unfortunately during most of the war adequate test equipment was
commonly lacking; when it was present, it was often in charge of inade¬
quately trained maintenance personnel who did not appreciate the need
for using it regularly. Figure 15-2 shows the combined results of a

1 See Sec. 214.

2 See Secs. 3 8 and 3-9.

3 Sec. 2-12.

Fig. 15-1.—Relation between radar
performance deficit and available radar
range for various types of target.

592

EXAMPLES OF RADAR SYSTEM DESIGN

[Sec. 15-3

number of such surveys of ground, ship, and airborne 10-cm and 3-cm
radars during the years 1943 and 1944. The radar performance figure
of the average set tested was 14 or 15 db below the rated value for the
radar. Since a performance-figure deficit of 12 db results in cutting the
maximum range of the set on aircraft by a factor of 2 (Fig. 15T), poor
radar performance was responsible for a loss of more than half the
tactical usefulness of the systems tested. Figure 15-3 shows the findings
of a more recent (July 1945) survey covering 10-cm ship radars; it indi¬
cates that there had been no change for the better.

Such serious deficiencies in actual field radar performance emphasize
the fact that the use of test equipment to measure performance and to
trace down the causes of impaired performance had not been incorporated
into routine maintenance practice for most radar sets at the end of the

Fig. 15-2.—Radar performance surveys. Fig. 15-3.—Radar performance survey,

1943-1944. July 1945.

war. Such important losses in performance are glaringly inconsistent
with the great effort expended in radar design to attain high performance.
In the design of new equipment, it is essential to make careful provision
for adequate testing and trouble-shooting; in the use of existing equipment
it is equally important to be sure that routine maintenance procedure is
sufficient to keep the radar within a few decibels of rated performance.
The design and use of test equipment is treated in detail in Vol. 23 of
this series.

DESIGN OF A HIGH-PERFORMANCE RADAR FOR
AIR SURVEILLANCE AND CONTROL
15-3. Initial Planning and Objectives. Formulation of Requirements.
At a relatively early stage in the development of microwave techniques
consideration was given to the possibility of applying them to the problem
of long-range air surveillance. Greatly improved azimuth resolution,
minimization of ground “clutter,” and improved low-angle coverage were
the principal advantages that microwaves appeared to offer. The best

Sec. 15 3]

INITIAL PLANNING AND OBJECTIVES

593

output pulse powers were then low, receiver sensitivities were poor, and
system problems were not well understood. Coverage equal to or better
then that provided by the longer-wave equipment then in use or under
development appeared to be attainable only by means of extremely
high antenna gain.

As these ideas developed, microwave techniques were rapidly advanc¬
ing. Requirements for antenna gain and size were reduced to moderate
values, and finally computations supported by measurement showed that
a microwave system could satisfactorily meet the coverage problem.
Work was then initiated leading to the production of a ground radar,
which proved to be one of the most successful sets ever developed. Its
design characteristics were so well chosen that, even with the best
techniques available at the end of the war, it could not easily be surpassed
for air surveillance and control.

As in several other system developments involving great advances
over previous equipment, requirements on this set were not firmly
specified during the developmental stage. In many respects this freedom
from rigid requirements was advantageous. General objectives were
clear, the design men were well situated to draw freely for advice and
help on component specialists and on men familiar with operational needs,
and they were largely free to use their own ingenuity and judgment to
meet the many problems that were presented.

General Objectives .—The principal objectives can be stated simply as
follows: Coverage was considered to be important both as to maximum
detection range and as to the altitude region included, but resolution in
azimuth and in range were thought to be of comparable importance.
Where height information was desired, auxiliary height finders were to be
used; thus the radar beam could be fixed in elevation and swept contin¬
uously in azimuth by rotation of the antenna.

Estimates of detailed requirements were difficult to make in regard to
characteristics such as (1) accuracy of range and bearing values as deter¬
mined by methods of data presentation, (2) interval between “looks”
at the target as determined by the revolutions per minute of the antenna,
and (3) traffic-handling capacity as determined by the number and type of
indicators provided. The designers, however, adopted as a general policy
the improvement or extension beyond current practice of equipment
characteristics that determined the accuracy and speed of data presenta¬
tion and use. Care was also taken in the design to permit still greater
extension of these facilities by simple changes or additions.

Beam Shape in Elevation .—A large air-surveillance set must be
located on the ground or be elevated at most by a low tower to avoid
interference by local obstruction. The radar beam in its 360° sweep
may look over land, over water, or over both land and water. Figure 15-4

594

EXAMPLES OF RADAR SYSTEM DESIGN

[Sec. 15-3

shows the general form of beam shape that gi% r es the most desirable
type of coverage under these conditions. Its lower edge is determined
by the optical horizon, with corrections for atmospheric refraction and
interference due to surface reflection. At a distance d in land miles
from the radar set, the horizon height h in feet is given by h — jd 2 for
normal atmospheric refraction (neglecting the interference effect, which
is small for microwaves; see Sec. 213). Reduction of the blind region
below this lower edge by locating the set on high terrain may be advanta¬
geous where the coverage is largely over water, but for overland surveil¬
lance this recourse is severely limited because of permanent echoes,
which can mask out all return in regions where the radar beam is inter¬
cepted by land surfaces.

Fig. 15-4.—Desirable coverage for long-range air-surveillance radar.

In setting a desirable limit for the upper contour for detection of a
given type of aircraft it was necessary to balance the value of high
coverage against coverage in range, since adding to one subtracts from
the other unless the designer chooses to increase the complexity of the
equipment. For operations during World War II, provision for detection
of a four-engine plane at all altitudes up to 35,000 ft was desirable, and
this value was taken to determine the upper section CD of Fig. 15-4.
Increasing the elevation angle of section AD of the contour does not add
greatly to the radar coverage requirements, since the region is small;
but practical difficulties of antenna design are encountered. Since
close-in regions have been in the past largely masked out by permanent
echoes, an angle of 30° was considered acceptable. With the upper and
lower limits of the contour determined, the problem was now to push
the maximum range out to the best possible value.

A detection range of 180 miles for a four-engine aircraft appeared to
be the best that could be expected, and the contour thus determined is

Sec. 15-4]

THE RANGE EQUATION

595

not unduly difficult to fit by beam-shaping. Even greater coverage both
in range and height was known to be desirable, but it appeared to be
attainable only by excessive antenna size or by an excessive multiplicity
of separate radar beams, each with its own transmitter and receiver
system.

A microwave set with the coverage shown in Fig. 15-4 presented a
very difficult problem. Because of uncertainty in measurements and
in the outcome of component development, there was no firm assurance
that it could be met. The success of the undertaking, however, was not
dependent on meeting this coverage fully, since maximum range and
altitude values within 20 per cent of the values of Fig. 15-4 would have
represented a major advance over any previous equipment. Failure to
detect one heavy plane above 30,000 ft would have limited the utility of
the equipment for special problems, but, because of the practice of group
flying, the normal problem was much less severe.

Azimuth Beamwidth .—The usefulness of the radar set for surveillance
was expected to improve in traffic-handling capacity, in ability to
resolve closely spaced aircraft, in accuracy of data, and in reduction of
ground clutter, as the azimuth beamwidth was decreased. The desirable
lower limit was expected to be set only from considerations of a practical
upper limit to antenna size and requirements of mechanical accuracy.
Results obtained fully confirmed these conclusions for beamwidths down
to 1° at half power, but in a later section of this chapter we shall see that
qualifications may be introduced if future development is extended to
beams much narrower.

Miscellaneous Requirements .—Although limitations on size, complex¬
ity, weight, and power consumption could be subordinated to the require¬
ment for excellence in radar performance, the designers were fully aware
of the importance of practical limitations on these characteristics. It
was also well understood that without great care and effort to achieve
the utmost in simplicity, dependability, convenient facilities for test,
and ease of maintenance, the equipment might fail to give satisfactory
field service.

In computations leading to the choice of system parameters the
designers did not have the advantage of much information that is now
available, yet in practically every case their decisions were excellent.
The discussion of design now given will make use of up-to-date informa¬
tion not available to the designers. This procedure is helpful for clarity
of presentation and will make the analysis more generally applicable.

15-4. The Range Equation. —There will now be undertaken a detailed
discussion of considerations leading to the choice of values for the follow¬
ing system parameters: (1) pulse length, (2) pulse recurrence frequency,
(3) azimuth scanning rate, (4) azimuth beamwidth, (5) beam shape in

596

EXAMPLES OF RADAR SYSTEM DESIGN

[Sec. 15-5

elevation angle, and (6) wavelength. We shall make use of the equation
that gives the maximum detection range of a system as a function of the
system parameters.

The range equation (see Sec. 2-4) can be written as

where

P = pulse power
a = radar cross section of target

A = area of antenna aperture

/ is a dimensionless constant dependent on the efficiency of the
antenna aperture. It is equal to about 0.6 for a simple
paraboloidal reflector, and its value is approximately the same
for the parabolic cylinder used for the lower beam of the
set described here. If the reflector is distorted to spread the
beam, as was done for the upper beam of the set under consid¬
eration, A and / cannot be used in the normal way.

S mi* = minimum detectable signal power. It varies directly with the
bandwidth B of the receiver, assuming that B is properly
adjusted for the pulse length, and, to a good approximation
for the problem under consideration, it varies inversely with
the square root of the number of pulses per scan on the target.

Acceptable values for a and S mln are now reasonably well established,
and, since other quantities determining R can be readily measured,
Eq. (1) can be used with some confidence for an absolute determination
of range. The safer practice, however, is to compute coverage relative
to the range performance on similar targets of a system with a similar
scan, which has been carefully checked as to component performance.
This procedure will be followed, and Eq. (1) will be used only for the
relationships it establishes among the system parameters.

16-5. Choice of Pulse Length. —The pulse length is convenient for
first consideration since its relations with the other parameters are
relatively simple. It enters the range equation through its effect on the
value of Sminj this quantity normally varies inversely with pulse length
since the receiver bandwidth, if chosen for optimum performance, is an
inverse function of pulse length.

Before proceeding further with the analysis, a discussion of other
quantities that influence the value of <Smin will be useful. To a good
approximation for the problem under consideration, the value of Sait,
varies inversely with the square root of the number of pulses per scan on
the target.

Since N„ — — j

Sec. 15-5]

CHOICE OF PULSE LENGTH

597

where

N .o = the number of pulses per scan on the target,
v r = pulse recurrence frequency,

0 = azimuth beamwidth in degrees between half-power points, and
oi = scan rate in degrees per second,
we obtain the relation

From the preceding section we have

S ma « ^ (3)

where r is the pulse length.

From Eqs. (1), (2), and (3) we obtain

Rmn P y, T^V r ^,

holding other parameters constant, or

RL* « Prv y . (4)

The average power output is given by Prv r .

It is desirable to drive the transmitter of a high-performance ground-
based system at the highest pulse power and the highest average power
that it will safely withstand. The value of R„^ can then be increased by
an increase in pulse length and a corresponding reduction in the pulse
recurrence rate, leaving average power and pulse power fixed at their
highest safe values.

Limitations on pulse length are imposed by the following considera¬
tions :

1. The minimum range difference at which two targets can be resolved
varies directly with pulse length. With a 1-^isec pulse, aircraft
inseparable in azimuth can be resolved if they differ in range by
more than 164 yd plus a small distance which depends on the
characteristics of the receiver and the indicator. With a 5-jusec
pulse, this limit for resolution becomes 820 yd plus the same
additive constant.

2. The intensity of cloud return relative to signal return from planes
varies directly with pulse length (Sec. 3T0).

3. The coverage area obscured by ground clutter will increase as pulse
length is increased.

4. Magnetron behavior has been found to become more critical, and
requirements on the voltage pulse from the modulator to become
more exacting, with increasing pulse length.

598

EXAMPLES OF RADAR SYSTEM DESIGN

[Sec. 15-6

5. Effects of pulse interference are more difficult to eliminate if the
receiver bandwidth is narrow, as required for best sensitivity with
a long pulse.

6. If a reduction in the pulse recurrence frequency is required to
increase pulse length, the azimuth accuracy may be adversely
affected and means for the selective detection of moving targets
may be less effective (Chap. 16).

Consideration of all these points leads to the conclusion that a pulse
length greater than about 2 /xsec is to be avoided.

Upper limits imposed on pulse power and on the pulse recurrence
frequency have been such that a decrease in pulse length below 1 /isec
would require a decrease in average power below the maximum safe
value, resulting in a decrease of 7? m „. Further, as we shall see, a l-/*sec
pulse yields a discrimination in range which is, for most of the area
covered by the radar, roughly equal to the azimuth discrimination
afforded by the beamwidth chosen. This is desirable from the stand¬
point of the indicator.

A pulse length of 1 nsec was finally chosen for the following reasons:

1. Average power output was pushed to the safe upper limit for the
transmitter with a value of 750 kw for pulse power, a pulse recur¬
rence frequency of 400, and a 1-nsec pulse length.

2. Reduction of the pulse recurrence frequency to 200 with a corre¬
sponding increase of pulse length to 2 nsec would have given an
appreciable increase in if this change led to no reduction in
pulse power or in average power. Since the magnetron then
available performed better both in pulse power and in average
power at 1 /xsec than at 2 fisec, the realization of any improvement
in would have been doubtful.

3. The many advantages of a short pulse were thought to outweigh
any small increase in coverage which a longer pulse appeared to
offer.

16-6. Pulse Recurrence Frequency. —The requirement of an adequate
time interval for presentation of data usually serves to set the upper
limit to the pulse recurrence frequency. Sufficient indicator sweep-time
must be provided to present signals without overlapping out to approxi¬
mately the maximum range of detection. To the longest indicator
sweep-time desired must be added sufficient time for recovery of the
indicator sweep circuits, in order to arrive at the minimum time interval
between pulses. Additional allowance must be made for any departure
from regularity in modulator firing.

Presentation of a 200-mile range was desirable, giving a time interval
of 2140 jusec for the sweep. An additional 360 /jsec was added for indica-

Sec. 15-7]

AZIMUTH SCAN RATE

599

tor recovery and to allow for irregular firing of the rotary spark-gap
modulator, giving an average time interval of 2500 ^sec between pulses,
or a v r of 400. Thus, the value of v, was set close to the permissible
maximum for a radar set with a 200-mile range.

For some applications, presentation of greater range would have been
helpful. A pulse recurrence frequency of 350 or 300, permitting range
presentation to 250 or 300 miles, would have reduced R^ very little,
but the characteristics of the modulator chosen restricted v T to 400. A
value of v T of 350 or 300 would be desirable from the standpoint of indi¬
cator range presentation for a future radar system of this general type,
but two other factors favoring higher v r must be considered:

1. The limiting accuracy of azimuth-angle determinations is approxi¬
mately half of the angular separation between pulses. A scan
rate of 36°/sec with a v r of 400 gives an angular separation between
pulses of 0.09°. The contribution of this effect to azimuth error
would be about 0.045°, which is negligible for normal surveillance
and control. In operations requiring very precise control of
aircraft this error would be appreciable, and if it were doubled
by decreasing the v T to 200 the resulting error might be a handicap.

2. Cancellation of echoes from stationary objects by MTI means is
less effectively achieved as the number of pulses per scan on the
target (N«) decreases (Chap. 16). If the scan rate is 36°/sec, with
a beam width at half power of 1.0° and a v r of 400, AT will have a
value of 11, which is about the lower limit for satisfactory per¬
formance of MTI.

16-7. Azimuth Scan Rate. —Although the relation
Smin ~ Vazimuth scanning rate

was not yet established at the time of the development here described, it
was roughly understood; and it put a high premium on slow scanning
rates. Mechanical problems in connection with the antenna mount are
greatly simplified by a slow scan rate.

Strongly opposing these considerations is the operational need for
more complete and up-to-the-second information, in order to follow
continuously the movement of high-speed aircraft and to control their
movements intelligently. Control problems vary in difficulty from
that of a well-formed group of aircraft moving over a simple course to
that presented by the requirement for accurate following or control of
numerous aircraft moving over complex independent courses.

A plane flying 300 mph moves f mile in 10 sec, or 2-* miles in 30 sec.
Data at 30-sec intervals, as given by a scan rate of 2 rpm, was considered

600

EXAMPLES OF RADAR SYSTEM DESIGN

[Sec. 15-8

adequate for a simple tracking or control problem, but complex problems
clearly called for higher scan rates even at the expense of coverage.

Foreseeing a wide range of applications for the new radar equipment,
its designers provided an antenna drive by means of which the scanning
rate could be adjusted over the range from 1 to 6 rpm. For one wartime
application that involved only simple tracking and control problems
but put a high premium on range performance, a scan rate of 2 rpm was
used exclusively. Other sets, which were used for more complex prob¬
lems, were commonly run at 4 rpm. Operation at 6 rpm was very limited
because of mechanical difficulty.

There is now good evidence that a scan rate of 6 rpm is desirable for
complex tracking and control, and even higher rates should be advanta¬
geous. Mechanical difficulties at high scan rates and requirements for
high azimuth accuracy will probably conspire to set an upper limit on
future scanning rates. In fact rates above 6 rpm may be entirely ruled
out by these limitations.

16-8. Choice of Beam Shape. Azimuth Beamvridth .—The merits of
a narrow beam are so widely understood that they will not be discussed
in detail here. All microwave development is recognition of the impor¬
tance of angular resolution. As wavelength is decreased, beamwidths
obtainable with antennas of practical size are decreased. With the
development of a microwave ground radar, the beamwidth for a long-
range air surveillance set was pushed down by an order of magnitude from
values previously used for this application, and results were spectacularly
successful. The set described here had an antenna aperture 25 ft wide
and operated in the 10.7-cm wavelength region, giving a beamwidth of
approximately 1.0°.

It will be of interest to see how far development toward increasingly
sharper beams might usefully be carried, and to establish as closely as
possible the optimum beamwidth for a long-range air-surveillance set.
It can readily be shown that a lower limit, and therefore an optimum
value, exists, entirely apart from questions of mechanical difficulty.

A scanning rate of 36°/sec gives an angular motion of 0.07° between
transmission of a pulse and return of the echo from a target at 200-mile
range. If the beamwidth were much less than 0.07°, the antenna gain
for reception of the signal would be greatly below normal. For a beam-
width of about 0.15° or 0.2° this effect becomes negligible, and the limit
it sets on beamwidth is probably not of practical importance.

A similar and more important fundamental limitation on beamwidth
is determined by the requirement that at least one pulse hit the target
per scan, with the beam axis off in angle from the target by no more than
a small fraction of the beamwidth. At a scanning rate of 36°/sec
and a v, of 400, the angular separation between pulses is 0.09°, and for

Sec. 15-8]

CHOICE OF BEAM SHAPE

601

reasonable overlapping of pulses a beamwidth of 0.2° at half power might
be considered adequate.

In order to show clearly the effect of beamwidth on R^, it is neces¬
sary to reconsider the range equation [see Eq. (1)],

( Pit A 2 f V*

\-l7r.S ml , 1 \y

If we let A = H X W, where

H = height of antenna aperture,
W = width of antenna aperture,

we obtain

' Pnf L W 1 H 1

k 47TlSminX 2

With coverage requirements in height specified, the beamwidth in
elevation angle is fixed; therefore, H/\ is a constant. We then have

-*■(£)“

holding P and a constant, where

kl V 4tX* ) ’

which is now a constant.

From Eq. (2) we see that Smin is inversely proportional to the square
root of beamwidth 9. All other factors that enter into the value of S mi „
can now be considered as constants and we can therefore write

R^ = (7)

where K 2 is another constant. The beamwidth in radians is X/W to a
good approximation; substituting this expression for 0 we have

= A'jTFKxW. (8)

From Eq. (8) we see that if the beamwidth is sharpened by decreasing
the wavelength and holding the antenna width constant, decreases
slowly. The variation of /? maI with antenna width is comparatively
rapid. If the beamwidth is sharpened to the point where the number of
pulses per scan on the target (NJ) is smaller than about 10, Eq. (8) no
longer holds. Then 7? mal becomes a more rapid function of X and a
slower function of W. For values of A T » C less than about 5. the variation
of /?m.i with IT and X is given approximately by

= AVW'XK

( 9 )

602

EXAMPLES OF RADAR SYSTEM DESIGN

[Sec. 15-8

Further decrease of beamwidth below 1° should be advantageous
operationally, although improvements due to increased resolution may
not be as marked in this region as they were in the region above 1°. If
wavelength is decreased below the 10-cm region to sharpen the beam,
coverage requirements will become more difficult to meet, even with the
assumption that component performance is independent of wavelength.
Because of coverage demands and for other reasons to be discussed later,
a decrease of wavelength below about 8 cm to sharpen the beamwidth
does not appear desirable.

An increase of antenna width beyond 25 ft to sharpen the beam
would have the advantage of improving coverage, but the following
limitations would be encountered:

1. If the set is to be mobile or easily transportable, an antenna of
greater width is cumbersome. With proper construction, an
antenna perhaps 35 ft wide might be satisfactory.

2. The requirement (for good gain per unit area) that the reflector
shape shall not depart from the shape desired by more than about
0.1X becomes increasingly difficult to meet as antenna width is
increased beyond 25 ft. Xo difficulty was experienced in main¬
taining this tolcrance with a 25-ft reflector, but the tolerance problem
was found to be severe for an experimental 50-ft reflector con¬
structed for a particular application.

These experiences would indicate that an antenna width up to about
35 ft might be desirable. If a wavelength in the region from 8.0 cm to
8.5 cm were used with such an antenna, the beamwidth should be about
0.55°, which appears to be about the practical minimum.

Beam Shape in Elevation .—A beam or a multiple system of beams prop¬
erly shaped was required to fit as closely as possible the contour of Fig.
15 4. A beam of 3° width in elevation angle with a maximum range of
200 miles fits the desired contour well at long range. For best fit its axis
must be elevated about 1.0° above the horizontal. Computations
showed that, with antenna width chosen at it practical maximum and with
all components pushed to the limit in performance, the coverage as
shown in Fig. 15-5 for this 3° beam [Curve At was the best, that could be
obtained with a single system. An antenna aperture 8 ft high is required.

Close-in coverage could only be obtained by use of a second system
which included transmitter, receiver, and antenna, with antenna width
and all components the same as for the fir-t system. Under these
conditions an antenna height of 5 ft, with the lower edge of the reflector
distorted from its parabolic shape over a small region, gives the coverage
shown by Curve li. Fig. 15 5 Improved coverage could have been

Sec. 15-8]

CHOICE OF BEAM SHAPE

603

provided by addition of a third system, but the additional complexity
was thought to be operationally not worth its cost.

Reflection of radiation from the earth’s surface greatly influences
the radar beam characteristics in elevation angle, and such effects must
be given careful consideration. Over water, the reflection coefficient is
high for all wavelengths of interest for air surveillance, and for very small
angles of incidence it can be assumed to be 100 per cent. Over land,
the reflection coefficient varies markedly with detailed surface shape and
with the composition of the terrain, and in general increases with increas¬
ing wavelength. Adequate data are not available on the reflection
coefficient, but at wavelengths of 10 cm or less it is assumed to be normally
negligible, and at a few meters it is normally substantial.

with antenna rotating at 2 rpm. Effective antenna height is 100 ft. Target is a single

B-24,

The detailed effects of surface reflection which influence coverage are
very complex. Some of the more important effects and conclusions
are summarized below (see also Sec. 2T2).

1. If surface reflection is high, the lowest possible angle of coverage is
raised from the horizon to an angle a = X/2 h, where a is in radians
and h is the height of the antenna above the surface.

2. If surface reflection is low, radiation striking the surface is lost.
It is clearly desirable to minimize this loss by beam-shaping.

3. Over an angular region in elevation where reflected intensity
equals direct intensity, at the center of an interference lobe
is doubled, but midway between two lobes /’i,., = 0.

4. At long wavelengths (one meter or greater), the use of reflected
radiation reduces requirements on antenna size, but the nulls

604 EXAMPLES OF RADAR SYSTEM DESIGN [Sec. 15-9

between lobes and especially the null region below the lowest lobe
are sufficiently broad to handicap detection and tracking greatly.
Shaping of a radar beam to reduce to a satisfactorily low value the
percentage of energy striking the surface becomes impractical at
wavelengths about 25 cm.

5. At short wavelengths (10 cm or below), the angular separation
between lobes is small. Loss of tracking due to nulls will normally
occur only over short track distances and will not be as serious as it
is for long wavelengths. For a system that works at least partially
over land it is advisable, however, to minimize the radiation
striking the surface by beam-shaping, in order to reduce the waste
in energy. Antenna height required for satisfactory beam-shaping
is not excessive.

In the region of 25 cm, assessment of the influence of these effects
on the general performance of the equipment becomes difficult, but for a
high-performance set of general application the above considerations
indicate that the best coverage obtainable as a function of elevation
angle continues to improve with decreasing wavelength down to wave¬
lengths even below 10 cm.

16*9. Choice of Wavelength. —In the discussion of other parameters,
the consideration of wavelength was necessarily included; the many
factors influencing choice of wavelength will now be summarized.

Component development has been concentrated on particular wave¬
length bands. Development of a new wavelength region is so costly in
technical effort and time that the wavelength chosen for a new system
must ordinarily lie in a region already exploited. Of the wavelength
regions in use, development in one may be further advanced than in
another, or inherent capabilities in one may be better than in another.
These considerations will influence the choice of wavelength.

Excluding the state of component development, the most important
factors that influence choice of wavelength are summarized below.

1. Beam characteristics in elevation angle. From previous dis¬
cussions it was concluded that the best obtainable beam character¬
istics in elevation angle improve with decreasing wavelength. At
wavelengths greater than about 25 cm, beam-shaping to eliminate
the undesirable effects of radiation striking the earth’s surface is
no longer feasible.

2. Coverage. If characteristics other than antenna height are held
constant, then maximum detection range decreases slowly as
wavelength decreases, but the antenna height required for the
maintenance of a given elevation coverage varies directly with
wavelength.

Sec. 15-9]

CHOICE OF WAVELENGTH

605

3. Beamwidth. Regardless of wavelength choice, the maximum
antenna width for a transportable air-surveillance set appears to
be about 35 ft. The minimum width, as determined by coverage
requirements, is probably about 25 ft. A beamwidth of 1° or less
is desirable if MTI requirements are ignored, and the most desirable
wavelength would then appear to be in the 10-cm region or even
shorter. Provision for MTI requires that the azimuth beam-
width be 1° or more, and 10 cm then becomes about the minimum
wavelength.

4. Atmospheric effects. Atmospheric absorption and variations in
refraction can be neglected over the wavelength region under
consideration, but the scattering of radiation from water droplets
giving rise to echoes from stornj centers is an effect of consider¬
able importance (Sec. 310). The scattering cross section of the
droplets responsible for the signal return varies as 1/X 4 . Return
from a large storm center also varies linearly with pulse length
and with beamwidth, but these parameters are restricted to
relatively narrow regions and the variation of cross section with
wavelength is therefore the controlling relation. Dependable
operational data are rather limited but the following results appear
to be established: (a)'At a wavelength of 3 cm, cloud return in
some regions frequently obscures a large fraction of the coverage
area and seriously restricts the use of the equipment; (6) reports
of this difficulty at 10 cm are less frequent, and information fur¬
nished on storm centers is valuable for direction of planes around
dangerous regions; (c) as wavelength is increased, less of the cover¬
age area is obscured by cloud return; but storm areas that are
dangerous to planes may fail to show on the radar at the longer
wavelengths.

The wavelength region between 8 cm and 25 cm appears to be best on
the basis of all these considerations. Though an optimum wavelength
cannot safely be specified, we can make three general remarks con¬
cerning the best wavelength for a long-range ground-based system for air
surveillance and control:

1. The choice of the 10-cm region for the set described here was
excellent, although a wavelength as short as 8 cm might have been
more desirable.

2. If MTI is to play an important role in future system performance,
and if improvement in MTI performance with increasing beam-
width is sufficiently great, longer wavelengths may be desirable.
The best wavelength may then become as great as 15 cm or even
20 cm.

606 EXAMPLES OF RADAR SYSTEM DESIGN [Sec. 15-10

3. The ultimate capabilities of radar components should not differ
greatly throughout the wavelength region from 8 cm to 25 cm.
Somewhat higher transmitter power will be available at the longer
wavelengths. At the time of the development described, perform¬
ance of existing components was better in the 10-cm region than
at any other wavelength suitable for this application.

15-10. Components Design.—The general system parameters chosen
as a result of considerations outlined in the last few sections are as follows:

Wavelength. 10.15 to 11.10 cm

Pulse length. 1 ;rsec

PH I' . 400 pps

Azimuth scan rate. 1 to 6 rpm

Antenna aperture, lower beam. 8 by 25 ft

Antenna aperture, upper beam. 5 by 25 ft

Beamwidth. 1°

It now remains to describe the components of the radar set.

The Antenna .—The antenna represented a departure from the usual
paraboloid of revolution which had been used for earlier microwave
antennas. It is described and illustrated in Sec. 9-12.

In the final design of the antenna mount, the reflectors for the upper
and lower beams are mounted back-to-back, so that their axes differ
by 180°. This complicates somewhat the mechanism for transmission
of azimuth-angle data from the antenna mount to the indicators. When
a given indicator is switched from upper-beam data to lower-beam data,
the mechanism controlling angular orientation of the sweep must be
suddenly shifted through a large angle. Operationally, on the other
hand, this arrangement was a considerable convenience. A given air¬
craft could frequently be seen in either beam, and by switching beams
every half-revolution of the antenna the operator could double the rate
at which he received plots.

More recent advances in antenna development have introduced
antenna types, other than the parabolic cylinder fed by a linear array,
which give the beam characteristics required for long-range surveillance
and control. The method that now appears most promising uses a
section of a paraboloid of revolution for the reflector. The periphery
of this surface is cut to give an aperture several times greater in width
than in height, and the reflector is fed by several horns or dipoles arranged
along a vertical line passing through the focus.

The latter antenna system 1 has the following advantages over the
linear array:

1 Similar antennas are described in Chap. 14, Vol. 12 of this series.

Sec. 1510]

COMPONENTS DESIGN

607

1. Azimuth angle of beams does not shift with a change in wave¬
length.

2. Multiple beams from separate transmitter-receiver systems can be
accurately set to the same azimuth angle. This property is very
desirable if the system is to be equipped for work with radar
beacons.

3. Open mesh or a grid structure can be used for the reflector surface
to reduce wind resistance. The linear-array system requires a
solid surface for the reflector, since the comparatively high gain
of the linear-array feed will give an objectionable back lobe
through mesh or gridwork.

The Modulator .—Because of its simplicity and power-handling
capacity, an a-c resonance-charging line-type modulator using a rotary

Modulator Spark gap

Space for blower 60 cps - 3p motor 4 qq cps generator phasing control inspection window

gap as a switching device was chosen. The rotary gap is mounted
directly on the shaft of a 400-cps alternator, which excites the network
and is properly phased by mechanical adjustment (Fig. 15-6). This
modulator choice was important in fixing the value of the PRF, but,
as already remarked, the desirable value lies in the neighborhood of
400 pps in any event.

Separate transmitters are used on the upper-beam and the lower-
beam systems; both are driven, through pulse transformers, from a
single modulator. The modulator is rated at 3000 kw.

R-f Components .—The high pulse powers used in this system demand
the use of waveguide for the r-f system. Each magnetron operates in a
field of 2800 gauss at 28 kv pulse voltage, drawing a current of about 30
amp and putting 750 kw of r-f power into the line at about 65 per cent
efficiency.

Crystal protection at this high power level is difficult, and a scheme
of “prepulsing” the TR tube is used. Part of the 8-kv modulator pulse

608

EXAMPLES OF RADAR SYSTEM DESIGN

[Sec. 15-10

delivered to the pulse transformer input is capacitively coupled to the
keep-alive connection of the TR tube. The delay in the pulse trans¬
former and magnetron is such that this pulse arrives at the TR tube
slightly before the r-f pulse arrives. This ensures that the TR tube will
fire, improving the crystal protection.

The complete duplexer assembly, which includes the magnetron, its
coaxial-output-to-waveguide adapter, the TR switch, the signal mixer,
and the AFC mixer, as well as a slotted section for SWR measurements, is
shown in Fig. 15-7.

The Receiver .—The receiver is conventional, with an i-f bandwidth
of 1.8 Mc/sec and an over-all gain of slightly more than 120 db. Instan-

Fig. 15-7.—Duplexing assembly. Two such units are included, one for upper-beam system
and one for lower-beam system.

taneous AGC circuits are provided and can be switched in or out at the
will of the operator. The AFC operates from a separate mixer and
amplifier and is of the hunt-lock type described in Sec. 12.7. Separate
receivers are used on the upper-beam and the lower-beam systems.

Indicator Equipment .—The set described here was based on the idea
that full flexibility is required in the indicator complement. Both
B-scopes and PPI displays can be used, in numbers and with geographical
coverage determined by the radar location, the density of targets, and
the mission performed by the set.

All data voltages and power voltages for the indicators are supplied
from a central point, the so-called “power console,” which houses the
antenna rotation controls, the transmitter switches, a servo-driven

Sec. 15-11]

MODIFICATIONS AND ADDITIONS

609

azimuth gear train that follows the rotation of the antenna mount, and
the information generator. The last-named unit contains the range-
mark generator (which produces signals 10 statute miles apart, with
every fifth one of greater magnitude than the others), a calibrating unit
for the range-mark generator, and a unit that generates from an azimuth
synchro signal the sawtooth voltage required to provide the azimuth
sweep for the B-scopes used with the set.

Azimuth marks 10° apart, with every third mark more intense, are
generated in the power console by means of a photoelectric device like
that shown in Fig. 13 34.

The B-scopes used are of the magnetic type described in Sec. 1314 and
illustrated in Fig. 13-43. PPI displays are of the rotating-coil type,
and are preferably arranged to permit off-centering. The rotating sweep
coil is driven by a size-5 synchro energized by a size-6 synchro connected
to the azimuth gear train in the power console. Two size-6 synchros
are driven by the azimuth gear train; they are set up 180° apart in angle.
One provides the drive for PPI displays on the upper antenna beam,
and the other for PPI displays on the lower antenna beam.

16-11. Modifications and Additions. —The performance of the radar
as finally built was excellent. Some of the PPI photographs in this
book, such as Figs. 6-5 and 17-21, show the long range, good definition,
and relative freedom from ground clutter which characterize the set.

By the time the set was built and ready for use, the need for it in its
originally planned role as a long-range air-warning set had nearly dis¬
appeared. The usefulness of such a set in controlling offensive air
operations was just beginning to be realized (Sec. 7-6). Accordingly
the radar, which had originally been intended for air warning from a fixed
site, was provided with facilities, sketched in Sec. 7-6, which made it
suitable as a mobile radar control center for use in offensive air warfare.

Apart from the addition of a greater number of indicators than would
have been needed for simple air warning, and the provision of off-center
PPI’s for the use of controllers, the modifications made in the set itself
to fit it for its control function were not extensive or important. Another
change in the set, also dictated by operational experience, did result in
altering it substantially. This will now be described.

Modification for Beacon Use .—The usefulness of ground radar for
aircraft control can be greatly extended by modifications that permit it
to work with airborne beacons (Chap. 8) mounted in the aircraft to be
controlled. Three principal advantages are offered by such a step:

1. Range extension. The useful range against single small aircraft
of the set described here is about 90 miles; this can be increased by
the use of beacons to the limit of the radar horizon (about 200
miles for an aircraft at 25,000 ft).

610 EXAMPLES OF RADAR SYSTEM DESIGN [Sec. 15-11

2. Positive identification. Aircraft control is frequently complicated
by the large number of aircraft operating at the same time within
range of a single radar set. Departure of aircraft from planned
flight schedules makes reliance on movements information unsatis¬
factory for identification. A beacon can afford positive identifi¬
cation of the aircraft carrying it.

3. Freedom from ground clutter. By having the beacon reply at a
frequency different from that used by the radar for interrogation,
the beacon replies can be displayed without any confusing radar
echoes.

Fig. 15-8.—Beacon receiving antenna mounted above lower-beam radar antenna.

Airborne beacons have been provided, almost without exception, with
vertically polarized antennas. They will thus work with the lower beam
of the set just described, but not with the upper beam since the latter is
horizontally polarized. The beacon is arranged to be triggered by the
pulses from the radar, but it replies on a different frequency, to receive
which an entirely separate beacon receiving antenna and receiver system
are provided. The beacon antenna, mounted on top of the lower-beam
radar antenna, is shown in Fig. 15-8. It is a horn-fed paraboloid cut to
8 ft by 4 ft. Despite the greater beamwidth of the beacon antenna than
that of the radar antenna, the beacon signals are almost as narrow in

Sec. 15-12]

DESIGN OBJECTIVES AND LIMITATIONS

611

azimuth as radar signals, since the beacon is triggered only over the nar¬
row beam of the radar antenna used for transmitting the beacon challenge.

The beacon receiver has a separate local oscillator and an i-f band¬
width of 10 Me/sec, to allow for differences in frequency among beacon
transmitters in the various aircraft. It is provided with sensitivity¬
time control (Sec. 12-8). The video output signals of the beacon receiver
go to a video mixer with controls so arranged that the indicator will
display either radar signals alone, radar and beacon signals together,
or beacon signals alone.

DESIGN OF A LIGHTWEIGHT AIRBORNE RADAR FOR NAVIGATION

The next example of radar system design to be described could scarcely
be more different. In the design of the ground radar set described, every¬
thing was subordinated to attaining the best possible performance;
in the AX/APS-10, the set now to be described, performance was impor¬
tant, as always, but it had to be attained within a variety of strict
limitations. These limitations dealt with total weight, size, and power
consumption, and with the required simplicity of operation, main¬
tenance, and repair. With its communications and height-finding
facilities, the total weight of an installation of the ground radar comes to
66 tons; the AN/APS-10 is made up of a few simple units whose total
weight is scarcely 120 pounds.

16-12. Design Objectives and Limitations. —By the year 1943, it was
clear that airborne radar could offer an extremely important air-naviga¬
tional facility. Long-wave airborne radar then in use for sea search
(Sec. 6-13) could be used for navigation in the vicinity of coastlines, but
interpretation of its type L display required long training even under the
best circumstances, and was impossible over land, where the multiplicity
of echo signals was hopelessly confusing.

Microwave airborne radar with PPI display was just coming into
large-scale use, and it was clear that the picture of the ground afforded
by such equipment would be a useful navigational aid over any sort
of terrain except the open sea. Further, microwave beacons could pro¬
vide fixed landmarks visible and identifiable at long range. However,
the microwave airborne radar sets then in existence had been designed for
some specific wartime operational requirement, such as sea search,
aircraft interception, or blind bombing. In consequence, their very
considerable weight and bulk (arising from the youth of the microwave
radar art) were not regarded as serious drawbacks. The radar was
necessary in any case to enable the aircraft carrying it to perform its
mission, and the navigational use of the radar was only incidental to its
main purpose.

Nevertheless, the clarity and convenience of the map-like presentation

612

EXAMPLES OF RADAR SYSTEM DESIGN

[Sec. 15-12

of microwave radar suggested that if such facilities could be incorporated
in aircraft whose primary mission had little to do with radar—transport
aircraft, for example—they could serve an important navigational
purpose. Since radar in this application is a very great convenience
rather than an imperative operational necessity, it must make the
minimum demands on the aircraft in terms of weight, drag, power con¬
sumption, and attention required from air and ground crew.

Existing microwave radar scarcely met these requirements in 1943.
For example, the AN/APQ-13, a bombing radar whose manufacture
was just beginning at the end of that year, has an installed weight of
620 lb without its special bombing facilities, and requires 100 amp of
28-volt aircraft power. It has 24 controls to be adjusted, omitting those
concerned with its bombing function. Forty-two cables are required to
interconnect its 19 separate component boxes. It is clearly uneconomic
to install such an equipment as one of several navigational aids in an
aircraft whose primary mission is not high-altitude bombing.

Thus, the design of a new set for this navigational use was indicated;
and it appeared that by careful attention to every detail such a set might
be made simple enough, light enough, and convenient enough to come
into widespread use. The equipment that resulted is the AN/APS-10.

Performance Requirements .—As always, the range performance of the
radar was the principal initial requirement. The following ranges
(in nautical miles) on various targets were taken as being comfortably
over the minimum necessary for navigation even of a high-speed airplane.

Ground painting. 25 to 30

Cities. 30 to 50

Storm clouds. 10 to 40

Mountains. 25 to 30

5000-ton ship. 25

Ground beacons. 150 (if not limited by horizon)

Portable ground beacons (low power).. 115 (if not limited by horizon)

Since rearward vision is usually as important in radar navigation
as forward vision, it was concluded that the set should have a full 360°
azimuth scan. In order that the appearance and location of nearby
targets should not change too much between scans in an airplane traveling
4 to 6 miles/min, only a few seconds could be allowed per scanner rota¬
tion. On the other hand, a reasonable number of pulses per beamwidth
had to be allowed.

Requirements on the antenna pattern were relatively simple. The
beamwidth in azimuth had to be as narrow as possible, to afford good
resolution of targets on the ground. The elevation pattern was required
to give the most uniform ground coverage possible throughout the normal
flying altitudes: from 1000 to 10,000 ft.

Sec. 1512] DESIGN OBJECTIVES AND LIMITATIONS 613

Limitations Imposed by Aircraft Installation .—The performance
requirements just mentioned can be simply stated, and it is easy to
check whether the completed radar meets them successfully. Neither
of these remarks applies to the extremely important set of design limita¬
tions that arise from the fact that the radar is to be used in aircraft.
The more important of these limitations are mentioned below.

The outstanding requirement is for low total weight. Every part
of the design is influenced by the necessity for making the final weight
of the radar as small as possible.

Low power consumption is important. Many aircraft types have
relatively low electrical-generating capacity, and it is most desirable
to be able to install a radar meant primarily as a navigational aid without
the necessity of revising the electrical installation of the aircraft. The
set must be able to operate either from a fixed-frequency 400-cps motor-
alternator set, or from a variable-frequency engine-driven alternator,
which may supply power at a frequency as high as 2400 cps.

Aerodynamic drag produced by the antenna housing must be as low as
possible. This requirement puts a great premium on as small an antenna
as possible. Taken in conjunction with the requirement for a narrow
beam, this means that the wavelength on which the radar operates
should be as short as is practicable.

Ease of installation in all types of aircraft is important. This suggests
that the radar be built in the form of several small components instead
of one or two large units, since small units afford greater flexibility in
installation. Maintenance is also simplified by dividing the equipment
into units that can be replaced for checking and removed for repair.
The necessity for connecting such units with cables adds considerably
to the total weight of the set, however, and the physical layout must be
carefully planned to reduce the number of cables and to keep their
lengths as small as possible.

Equipment mounted in aircraft is subject to extreme variations of
pressure and temperature. External air pressure can vary from that at
sea level to the pressure of less than one-quarter atmosphere found at
30,000 ft. At the reduced pressures of high altitude, clearances required
to prevent arc-over from high-voltage points are likely to become exces¬
sive. Further, the low temperatures of high altitude are likely to cause
condensation, in the r-f line, of the water vapor that is present in warm
sea-level air. The simplest solution for these difficulties is to seal the
transmitter and the r-f line pressure-tight so that they can be main¬
tained at sea-level pressure at any altitude.

Such pressurization of the modulator and the r-f system increases
the problems of cooling. To meet operating conditions on the ground
in the tropics, the radar must operate indefinitely at an ambient tem-

614

EXAMPLES OF RADAR SYSTEM DESIGN

[Sec. 15-13

perature of 50°C, and must withstand an hour’s operation at 71°C. At
the same time, because of the low temperatures at high altitude, the set
must work satisfactorily at — 55°C.

Severe vibration and shock are encountered in aircraft, and some of
the weight of an airborne radar must be spent on adequate shock-
isolating mountings.

Not only must the rectifier-filter power supplies for the radar circuits
operate at any frequency from 400 to 2400 cps; they must also tolerate
poor voltage regulation and poor waveform in the primary power supply.

The presence in the same aircraft of high-power radio transmitters,
sensitive radio receivers, and a high-voltage ignition system makes it
necessary to shield and filter the radar set adequately to prevent it from
interfering with other equipment, and to protect it from interference
arising in other equipment.

Limitations Imposed by Personnel .—A radar for navigational use in
all sorts of aircraft must be manufactured in great quantity with ease
and economy, must be so simple to use and understand that only a short
period of training is necessary to operate it adequately, and must be so
easy to maintain that it can be kept in satisfactory condition with little
maintenance effort. Whereas, in principle, the operators of such a
specialized radar as a blind-bombing device could be highly trained
(though, in point of fact, few were, in the war), the operators of this
navigational set were not primarily concerned with learning to operate
it properly. Its own simplicity had to be great enough so that its
operation was no more difficult to master than that, for example, of the
radio compass.

15-13. General Design of the AN/APS-10 .—In the framework of
these performance requirements and design limitations, the design of the
AN/APS-10 was attempted. The most important decision concerned
the wavelength to be used. At the outset, experiments were made with a
simple PPI radar based on the 10-cm lighthouse-tube transmitter-
receiver unit used in the AN/APG-15 (Sec. 6-14), using an antenna of
20-in. diameter. It was found that the range performance was marginal.
Worse, the resolution of the set was so low that excessive skill in interpre¬
tation was needed to navigate with the set in the absence of well-defined
geographical features. Since the larger antenna required to improve
both the range and the resolution of this set could not be housed in
aircraft without creating excessive drag, it seemed clear that a shorter
wavelength would have to be used for general navigation.

The other bands at which components had been developed were
around 3.2 cm and 1.25 cm. The 1-cm art was in a very early
state, and equipment was still cumbersome and of poor performance.
For this reason, 3.2 cm was chosen. This was a fortunate choice; for

Sec. 1513]

GENERAL DESIGN OF THE AN/APS-10

615

although it was not then known, the absorption of 1.25-cm radiation in
water vapor is so strong as to remove almost entirely the usefulness of
this wavelength for navigational purposes.

Next, a decision had to be taken regarding the pulse power. High
pulse power is very costly in the design of radar for aircraft, both in
terms of the primary power requirement and in terms of total weight. 1
A comparison with the performance of the AN/APQ-13 served as a guide
in determining the pulse power of the AN/APS-10. The AN/APQ-13,
using about 50-kw pulse power and a high-altitude cosecant-squared
antenna of gain 950, showed a range of about 45 miles for general ground
painting and 50 to 100 miles on cities. Its receiver had a sensitivity of
about 5 X 10~ 13 watts for a signal equal to noise.

The 45-mile ground-painting range of the AN/APQ-13, as compared
with the 25 miles required of the AN/APS-10, allowed a 10-db reduction
of transmitter power for the latter, if the antenna gain and the receiver
sensitivity were kept the same. However, it was felt that a 30-in.
antenna was too large to be tolerated for the AN/APS-10. Experiments
showed that an 18-in. cosecant-squared antenna designed for an altitude
of 7000 ft would be useful in the usual altitude range from 1000 to 10,000 ft
without unduly overilluminating short-range targets at low altitude or
causing too serious a hole in the center of the pattern at altitudes higher
than 7000 ft. This antenna proved to have a gain of 700; this meant
that the reduction of antenna gain would require about 3 db of the
calculated 10-db leeway between the AN/APQ-13 and the AN/APS-10.

The remaining 7 db could be and were used to permit a reduction
in pulse power. The lightweight, low-voltage 2J42 magnetron (see
Fig. 10-46) was used in the AN/APS-10, giving an output pulse power of
10 kw. The lower voltage and lower power required by this tube enabled
the design of an extremely compact and simple pulser, shown in Fig. 10-47.

Since the whole of the 10-db differential between the two sets had
been used up in the smaller antenna and the lower pulse power of the
AN/APS-10, it was necessary to make sure that the receiver sensitivity
of the latter set did not fall below that of the AN/APQ-13. Further,
special pains had to be taken to provide good range performance against
microwave beacons. In the AN/APQ-13, the TR-switch tuning was not
changed from search to beacon operation, and a narrow-band ATR was
used. The loss of beacon signal in the TR and ATR alone could be as
much as 15 or 20 db. In addition, no automatic frequency control of the
beacon local oscillator was provided. Better facilities for working w r ith
beacons were desired in the AN/APS-10.

1 W. L. Myers, “ Weight Analysis of Airborne Radar Sets,” RL Report No. 450,
Jan. 1, 1945.

616

EXAMPLES OF RADAR SYSTEM DESIGN

[Sec. 15-14

Antenna

Transmitter-receiver

Indicator

Sychronizer

Fig. 15-9.—Units of AN/APS-10.

only the final result will be presented, and an attempt made to rationalize
it in terms of the considerations of Sec. 15-12.

A photograph of the components of the set is shown as Fig. 15-9.
Figure 15-10 is a schematic diagram of the various units and their major
subassemblies. The set consists of five major units: a transmitter-
receiver, a synchronizer, a synchronizer power supply, a scanner, and an
indicator. There are two minor components, a trim-control box and a

15-14. Detailed Design of the AN/APS-10. —With these major
design decisions taken, the detailed components design of the AN/APS-10
remained. No attempt will be made to discuss the many interacting
decisions that determined the design of the components of the set;

Sychronizer
power supply

Modulator
and magnetron

Synchronizer
power supply

Fig. 1510.—Block diagram of AN/APS-10 system.

Table 15T.— Units of the AN/APS-10

Unit

Weight

Weight of
mounting

A-c power,
watts

D-c

power,

watts

Maximum over-all
dimensions of units,
in.

Pressuriza¬

tion

Transmitter-receiver.

46 lb

4 lb

185

15-20

12|

12!

20A

Yes

Synchronizer.

13 lb 1 oz

13 oz

14!

Synchronizer power supply.

19 lb 7 oz

1 lb 4 oz

150

Scanner *.

20 lb

20-30

line pressur-

ized

Indicator and visor.

8 lb 5 oz

5 oz 1

Included

13!

with sync.

6 lb

Trim control indicator and flexible shaft.

2 lb 6 oz

* These figures apply to the standard AN/APS-10 scanner. A special lightweight (13 lb) scanner, suitable for most applications, was also developed for
AN/APS-10. (See Sec. 9-12 and Fig. 9 - 16.)

618 EXAMPLES OF RADAR SYSTEM DESIGN [Sec. 15 14

Sec. 1514]

DETAILED DESIGN OF THE AN/APS-10

619

pressure pump. The weight, power consumption, and size of the units
are summarized in Table 15T. Table 15-2 gives more detail on the
design of the various units.

The transmitter-receiver unit contains the magnetron, the modulator
and its power supply, the duplexer, the TR switch, the mixer, and the
local oscillators, as well as a motor-driven time-delay switch for modulator
turn- on, and a trigger amplifier for the modulator. The receiver strip,

Table 15-2.—-Detailed Specifications of the AN/APS-10

Total weight of units and mountings. 124* lb less cables

Primary power required

Alternating current. 115 V. 400-2400 cps, 340 watts

Direct current. 27.5 v, 80 watts

Over-all system performance

Transmitter frequency. 9375 + 55 Me/sec

Pulse power. 10 kw

Receiver sensitivity, search. 131 db below 1 watt

Receiver sensitivity, beacon. 125 db below 1 watt

Pass band of untuned r-f components. 9280 + 185 Mc/sec

Modulator

Type. Line-type with hydrogen thyratron

PRF, search. 810 pps

PRF, beacon. 405 pps

Pulse length, search.. 0.8 /nsec

Pulse length, beacon.. 2.2 nsec

Receiver

Intermediate frequency. 30 Mc/sec

Bandwidth of i-f amplifier. 5.5 +1.0 Mc/sec

Indicator

Type (Sec. 13-17). 5-in. resolved-current PPI

Focus. Permanent magnet

Cathode-ray tube. 5FP14 (or 5FP7)

Video bandwidth. 3 Mc/sec

Antenna

Reflector. 18-in. paraboloid; / = 5.67 in;

7000-ft cosecant-squared pattern

Feed. Two-dipole type

Gain. 700

Polarization. Florizontal

Azimuth beamwidth..
Scanner

Scan rate.

Tilt angle.

Trim angle.

Number of tubes
Transmitter-receiver. .

Synchronizer.

Indicator.

Rectifier power supply

5°

30 rpm

0° to -18°

6|° to —10j°

31 tubes and 3 crystals
25

* With standard scanner. Lightweight scanner reduces total weight to 117 lb.

Fiq. 1511.—AN/APS-10 low-altitude PPI.
Washington, D. C. at 0°, 8 to 13 miles, (a)

(b)

Fig. 16-12.—AN/APS-10 medium-altitude PPI. Special 30-in. antenna used. Range
marks 10 miles apart; altitude 6000 ft.; Narragansett Bay at 350°, 20 to 30 miles; Long
Island at 160°, 20 to 40 miles, (a) Photograph of scope. (6) Sketch from map.

621

622

EXAMPLES OF RADAR SYSTEM DESIGN

[Sec. 1514

(containing the i-f amplifier, the detector, and a video output stage), the
automatic frequency control unit, and the low-voltage power supply for
these circuits, are also mounted in this unit. The detailed design of this
receiver is treated in Sec. 1210.

The synchronizer unit includes the primary timing circuits, and the
sweep, range-mark, and intensifier circuits. On its front panel are the
operating controls for the system. This unit serves as a cable junction
box, and its use in this capacity has enabled the set to be designed with a
total of only seven cables. Since the circuits are designed to allow for
cable capacitance and for voltage drops, any of these cables can be as
long as 25 ft. Separation of the synchronizer power-supply unit from
the synchronizer itself permits the latter to be small enough to be con¬
veniently used as the main control box. It can be mounted with the
control panel either vertical or horizontal, as each installation may
demand.

The indicator unit contains a video amplifier, in addition to the
cathode-ray tube and its deflection yoke and focus magnet.

The synchronizer power supply provides the necessary voltages for
the indicator and the synchronizer.

Performance of the AN/APS- 10.—The completed set shows per¬
formance meeting the initial requirements. Scope-map comparisons
that display the usual overland performance of the set at low and medium
altitude are shown in Figs. 15-11 and 15-12. The blanked-out sectors
abeam are due to shadows cast by the engine nacelles of the C-47 aircraft
in which the set was installed. Figure 15-12 was taken while a special
experimental antenna of 30-in. horizontal aperture was in use; thus the
azimuth resolution and range performance are better than those attained
with the standard 18-in. antenna.

The performance of the set with 3-cm beacons is especially good
because careful attention was paid to the radar-beacon problem in design.
The major changes involved in switching from search to beacon operation
are:

1. Change of pulse length from 0.8 to 2.2 *isec.

2. Change of PRF from 810 to 405 pps.

3. Change of TR-switch resonant frequency from the magnetron
frequency to the beacon frequency.

4. Change from search to beacon local oscillator.

5. Change from search to beacon AFC. (Sec. 12-7.)

6. Stretching of beacon reply pulses in the video amplifier.

A broadband ATR tube is used primarily to pass beacon signals with
minimum loss, and a wider i-f band than necessary for optimal signal-to-

Sec. 15-14]

DETAILED DESIGN OF THE AN/APS-10

623

noise ratio is employed to insure reception of signals even from beacons
that have drifted off frequency.

The long (2.2-gsec) pulse necessary for beacon triggering required a
reduction in PRF in order to keep the duty ratio of the modulator nearly
that used for search. The PRF of 810 used in search was set by the
requirements of the indicator circuit; it is halved for beacon operation.

Fig. 15-13. —Beacon replies on AN/APS-10 scope. Range marks 20 miles apart.

At a repetition rate of 405 pps with a 5° beam, five to six effective
pulses are sent to a beacon per scan, since only half the pulses incident
on the beacon are effective because of its switched local oscillator (Vol.
3, Sec. 8-13). Figure 15-13 shows the responses from four beacons
appearing at once on the indicator of an AN/APS-10 radar.

Suitability for Aircraft Installation .—The low power consumption and
low weight of the AN/APS-10 are shown in Tables 15-1 and 15-2. The

624

EXAMPLES OF RADAR SYSTEM DESIGN

[Sec. 15-14

net weight of the components is about 120 lb. To this must be added 12
lb for cables and brackets, 28 lb for an inverter, and 25 lb for a radome,
so that the installed weight of the set is about 185 lb, well under a third
that of the AN/APQ-13. Snap fasteners and spring-loaded bands are
used as retaining elements to facilitate the removal and replacement of
units.

To achieve low weight and simplicity, many attractive design features
had to be sacrificed, including antenna stabilization, sector scan, ground-
range sweeps, and long pulses for maximum range performance. The
possibility of adding to the AN/APS-10 special units to perform special
functions has, however, been retained. A trigger pulse and video signals
are available for any attachment, as are provisions for an additional
azimuth-angle take-off and means for externally reversing the azimuth
scan motor.

Adequate filtering and shielding are provided to deal with any
ordinary problems of mutual interference between the radar and other
electronic equipment installed in the same aircraft.

The transmitter-receiver is protected against changes in external
pressure by means of a rubber-gasket seal and pressure-tight cable
connectors. The r-f line is also sealed and is connected to a pressure
pump with a dryer oil its intake.

Internal and external fans are provided for the unit in which there
is the greatest heat dissipation—the transmitter-receiver. The internal
rise above ambient temperature in this unit is 35°C.

All units except the scanner are shock-mounted. The r-f line between
the shock-mounted transmitter-receiver and the rigidly attached scanner
has a pressure-tight flexible section. Where possible, as in the case of the
transmitter-receiver, center-of-gravity shock mounts are used.

To minimize the effect of variations in supply voltage and waveform,
full-wave rectifier power supplies with choke-input filters are used
throughout the set. Electronic regulation of voltage has been used
where necessary to maintain precise voltage or to remove the low-
frequency ripple found in the output voltage of many aircraft alternators.

Operational Suitability .—In contrast to the 24 controls of the AN/-
APQ-13, the AN/APS-10 has only 10. Four must be used often, four
infrequently, and the remaining two are primarily for the convenience
of the operator. The four commonly used controls are:

1. A range-selector switch that enables the operator to choose either
a continuously variable, 4- to 25-mile sweep or a 50-mile sweep for
search operation, or a 0- to 90-mile or 70- to 160-mile sweep
primarily intended for beacon operation. Two-mile range marks
are provided on sweeps shorter than 14 miles, 10-mile marks on

Sec. 1514]

DETAILED DESIGX OF THE AX/APS-10

625

sweeps between 15 and 50 miles, and 20-mile marks on the beacon
sweeps.

2. A receiver gain control.

3. A tilt control for the antenna. This enables adjustment of the
depression angle of the radar beam to the optimal value for any
altitude. A tilt meter calibrated in altitude is provided; it serves
as an approximate guide to the correct setting.

4. A search-beacon switch.

The controls less often used are:

1. The off-on switch.

2. The focus control of the indicator.

3. The brilliance control of the indicator.

4. The trim control. This enables the operator to adjust the scanner
mechanism in pitch so as to keep the axis of the scanner vertical
despite changing attitude in flight due, for example, to consumption
of fuel. A fore-and-aft bubble level and a hand crank connected
by flexible shaft to the scanner are provided.

The two “convenience” controls are the adjustments for range-mark
intensity and for dial-light brilliance.

The operation of the AX/APS-10 is so simple that an hour’s flight
experience is sufficient to qualify a navigator to adjust and use the set.

For ease in maintenance, all units of the set have been made inde¬
pendently replaceable, with no need of adjustment for individual units.
Even within the major units of the set, subassemblies have been designed
for replacement in the event of failure.

External test points'have been provided on the transmitter-receiver
and the synchronizer power supply to aid in identifying defective units
in cases of failure. On the transmitter-receiver these include a test
trigger from the modulator, an extra video channel, and a lead from a
directional coupler which enables r-f checking. On the synchronizer
power supply pin jacks are provided to permit measurement of power-
supply voltages. Other test points are incorporated on many of the
subchasses of the transmitter-receiver unit. These external test points
permit a routine procedure of inspection and preventive maintenance to
detect incipient failure and insure peak performance.

The consensus of its users is that the AN/APS-10 fits its requirements
well. Further improvement in lightness, convenience, and modesty of
power demand will follow on general advance in the art, and in particular
on detailed attention to component design. To mention one example,
the substitution of subminiature tubes for larger standard types will
reduce bulk, weight, and power consumption.

CHAPTER 16

MOVING-TARGET INDICATION

By A. G. Emslle and R. A. McConnell

INTRODUCTION

16*1. The Role of Moving-target Indication. —The object of moving-
target indication (MTI) is to present the signals received by a pulse
radar set in such a way that moving targets show up while stationary
objects give no response. The most advanced method of doing this
allows the moving targets to be presented on a PPI. Figure 16T shows
two PPI photographs, one with MTI in operation and one without,
taken on a ground radar set at Bedford, Mass., using a wavelength of 10.7
cm and a PRF of 300. The removal of the ground clutter is seen to be
complete. The photographs in Fig. 16-2 were taken at Boston, Mass.,
where, because of screening by a ring of low hills, clutter does not extend
appreciably beyond 10 miles. In these photographs, taken on a set
having a wavelength of 10.7 cm and a PRF of 1650, the effectiveness of
MTI in reducing storm echoes is shown.

The problem of MTI is somewhat more difficult and the results less
satisfactory when the radar set is carried on a moving ship or airplane
because the clutter to be eliminated is itself moving relative to the radar
set and the clear-cut distinction between moving and stationary targets is
lost. In spite of this, it is possible to arrange MTI so that vehicles
moving on the ground can be seen from an airplane. In the case of a
shipborne set it is possible to compensate for the ship’s own motion and
therefore to see other ships and aircraft in the presence of sea-clutter and
storm echoes.

16-2. Basic Principles of MTI. —Two fundamental ideas are involved
in the solution of the MTI problem: first, a method of reception that
responds differently to fixed and to moving targets; second, an arrange¬
ment that takes advantage of this difference by selecting only the moving
targets.

The method of reception always uses the doppler effect in one form
or another. The simplest arrangement is that shown in Fig. 16-3.
Power from the transmitter is mixed with the c-w echo from the target.
After detection, the beats between the two frequencies / and f can be

626

Sec. 16-2] BASIC PRINCIPLES OF MTI 627

628

MOVING-TARGET INDICATION

[Sec. 16-2

Fig. 16-2. —Successive 30-mile normal and MTI PPI photographs. Note storm echoes
at 10° at 25 miles, 60° at 15 miles, and 150° at 30 miles. Seven aircraft are visible on the
MTI PPI.

Sec. 16-2]

BASIC PRINCIPLES OF MTl

629

heard in the phones. The echo frequency is given by the well-known
doppler formula

The beat frequency is then

/«=/'

/ =

/•

Since the target velocity v is very small compared with the velocity of
light c, this can be written as

2v , _ 2v

~c r

For v in miles per hour and X in cm this becomes

See, for example, Fig. 5T2.

The arrangement of Fig. 16 3 gives no range information. This
can be remedied by chopping up the outgoing train of waves as in Fig.
16-4. The beats in the telephones now consist of a succession of pulses
whose envelope has the doppler frequency /<(. Note that the doppler
effect can be viewed as causing a phase shift of the echo from pulse to
pulse. It is easy to calculate this phase change and to show that it is
equivalent to the frequency shift. The distance traveled by the target
between pulses is vT, where T is the repetition period. Hence each
pulse travels a distance 2 vT less than the preceding pulse. This is
2vT /X wavelengths, so that the phase change is 2ir2vT /X between each
pulse and the next. The beat frequency is then 2r/X, as before.

630

MOVING-TARGET INDICATION

[Sec. 16-2

To obtain range information with the scheme of Fig. 16-4, the phones
can be replaced by an A-scope synchronized with the modulator. The
appearance of the A-scope is shown in Fig. 16-5, where one moving target

Fio. 16-4.—Doppler effect with pulsed system suitable for low frequencies.

is seen among several stationary ones. The butterfly-like appearance
of the moving target is the result of the variation in pulse amplitude as
shown in Fig. 16-4. Stationary targets exhibit constant phase from pulse

to pulse, and therefore a steady
amplitude.

The arrangement of Fig. 16-4
can be used at frequencies of a few
hundred megacycles per second but
is not practical at microwave fre¬
quencies in the absence of suitable
power amplifiers. However, the

Fig. 16-5.—Doppler beats on an A-
scope.

Fig. 16-6. —Doppler system for micro-
waves. Dotted lines show what must
be added to ordinary radar set.

same effect 1 can be obtained by the circuit of Fig. 16-6, which shows the
basic diagram of a microwave pulsed radar, with the addition of a reference
oscillator. This reference oscillator provides a c-w signal with which
to beat the incoming echoes. Since the transmitter starts with random
phase from pulse to pulse, it is necessary to match the phase of the refer¬
ence oscillator to that of the transmitter at each transmitted pulse.

1 "Second time around” echoes—signals received from the second preceding
pulse—will not be canceled by the arrangement of Fig. 16-6.

Sec. 16-2]

BASIC PRINCIPLES OF MTI

G31

Cancelled signals
2 minus 1-

Fig. 16-7. —Pulse-to-pulse cancellation.
The first four traces represent successive
sweeps of A-scope. The last three traces
show the canceled signals.

This can be done by allowing a sufficient amount of power from the trans¬
mitter to enter the resonant cavity of the oscillator, which is then forced
into step with the transmitter. This process is called “locking” the
phase of the oscillator, or making it “coherent.” The appearance of
the A-scope will be the same as that shown in Fig. 16-5.

Two methods of presenting
the doppler information have been
mentioned: the aural method
(Fig. 16-3), and the A-scope
method (Fig. 16-6). These indi¬
cators are useful only with a
stationary or very slowly rotating
antenna. At normal rates of
scanning, it is necessary to display
signals on a PPI in such a way
that only moving targets appear
on the scope. This can be done
by the method of pulse-to-pulse
cancellation illustrated in Fig.

16-7, where the first four traces
represent successive sweeps on

the A-scope of Fig. 16-5. The scheme is to delay the signals of
Sweep 1 for a whole repetition period and then subtract them from the
signals of Sweep 2. In the same way Sweep 2 is delayed and subtracted
from Sweep 3, and so on. The results are shown in the last three traces

of Fig. 16-7. This process can be
carried out continuously by the
arrangement of Fig. 16 8, in which
the signals are split into two chan¬
nels, one of which contains a super¬
sonic delay fine, and then brought
together again for cancellation.
An important practical point in the
use of this scheme is the degree to
wdiich the output signal of the delay line simulates the input signal, for
the fidelity of reproduction of signals by the delay line influences the
maximum clutter cancellation possible.

It is also possible to delay the signals by means of a “storage tube,”
which works in a manner related to that of the Iconoscope used in
television. The supersonic delay line was used as a delay device in the
MTI systems that have had the most thorough testing; its use is therefore
assumed in what follows. Certain advantages attend the use of a
storage tube, notably the ability to apply MTI to a system whose

Fig.

16 - 8 .—Cancellation of signals of con¬
stant pulse-to-pulse phase.

MOVING-TARGET INDICATION

632

ISec. 16-3

repetition rate has “time jitter” (see Vol. 19, Chap. 25 of the Radiation
Laboratory Series).

16-3. A Practical MTI System. —Figure 16-9 is a block diagram of a
practical MTI system. It can be regarded as a refinement of the arrange¬
ment of Fig. 16-6; instead of beating the signals with an r-f reference
signal, the same thing is now done at intermediate frequency. This is
accomplished by applying the superheterodyne principle both to the
locking pulse and to the signals. The same stable local oscillator pro¬
vides a signal to two mixers, one of which reduces the frequency of the
locking pulse, the other the frequency of the signals, to 30 Mc/sec.
The i-f locking pulse from the first mixer is applied to an i-f oscillator
which is thereby rendered coherent in phase with the locking pulse.

Fig. 16-9.—Practical MTI system.

The circuits of Figs. 16-6 and 16-9 are entirely equivalent as far as the
output of the receiver is concerned. The phase of the i-f echo signal
from a stationary target depends on the starting phase of the transmitter,
the starting phase of the local oscillator, and the range (which determines
the number of cycles executed by the local oscillator while the transmitted
pulse travels to the target and back). The i-f reference signal provided
by the coherent oscillator has a phase that depends on the starting
phases of the tr nsmitter and of the local oscillator, and on the range
(which determines the number of cycles executed by the coherent oscil¬
lator during the echo-time). The starting phases of the transmitter and
the local oscillator cancel out when the i-f echo signals and the i-f reference
signal beat against each other, so that the phase of the receiver output
depends only on the number of cycles executed by the local oscillator
and by the coherent oscillator. Both of these oscillators are made to be
stable; consequently the beat signal from a stationary target has a
steady amplitude from pulse to pulse. When the target is moving, its
range will change from pulse to pulse and a fluctuating output signal
results from the corresponding change in the phases traversed by the
oscillators during the echo-time.

Sec. 16-3]

A PRACTICAL MTI SYSTEM

633

A simple laboratory type of delay line is shown in Fig. 16-10. It
consists of a steel tube filled with mercury, with A”-cut quartz crystals
cemented to its ends by means of lacquer. An end cell filled with mercury
is attached to the outside of each crystal by the same method. When an
alternating voltage is applied across one of the crystals (that is, between
the mercury in the end cell and that in the tube), the crystal undergoes
periodic changes in thickness due to the piezoelectric effect. The
vibrations of the crystal are communicated to the mercury as a super¬
sonic wave which travels down the
tube at a speed of 4700 ft/sec,
corresponding to a delay of 17.6
jisec/in. On arriving at the other
end of the line the wave causes
the receiving crystal to vibrate,
and this vibration produces an
alternating voltage between the
faces of the crystal.

The mercury end cells, in addi¬
tion to acting as electrodes, serve
also to prevent reflection of the
supersonic wave by the crystals.

When the crystal is driven at its
resonant frequency, it acts as a
half-wave acoustical transformer; thus the delay line is properly termi¬
nated at each end by the end cells. The wave entering an end cell is
broken up and absorbed by the skew back of the cell.

A free quartz crystal has a very high Q and therefore such a narrow
bandwidth that it cannot transmit microsecond pulses. In the delay line,
the loading of the crystal by the mercury causes the crystal to be almost
critically damped—that is, to have a Q near unity. Thus the band¬
width of the crystal, when it is cut, for example, for 15 Mc/sec, is many
megacycles per second. The frequency response curve has its maximum
at the resonant frequency of the crystal and falls to zero at zero frequency.
Thus it is not possible to transmit video pulses directly through the delay
line without distortion. Instead, the pulses are used to modulate a
carrier whose frequency is that for which the crystal is resonant.

Figure 16-11 shows, in more detail than Fig. 16-8, the arrangement of
the cancellation circuits. The video signals from the MTI receiver
amplitude-modulate a 15-Mc/sec oscillator and amplifier of conventional
television design. Its output signals go to the input crystal of the
15-Mc/sec delay line, and also to the “undelaved” channel of a two-
channel amplifier. The “delayed” channel of the amplifier receives the
output signal from the delay line and amplifies it. The two channels of

Fig.

16-10.—Laboratory-typo supersonic de¬
lay line.

634

MOVING-TARGET INDICATION

[Sec. 16-3

the amplifier have separate diode detectors arranged to give opposite
signal polarities, so that the delayed and the undelayed signal can be
adjusted in amplitude to cancel each other when added. Since the video
signal from a moving target is bipolar (cf. Fig. 16-7), a rectifier is included
in the circuit ahead of the PPI.

In order to get good cancellation, the signals in the two channels of
the amplifier must match very closely in time. This means that the

Fig. 1611.—Block diagram of delay-line circuits.

pulse-repetition period has to match the delay time of the supersonic line
with great accuracy. The velocity of sound in mercury varies with the
temperature by about one part in 3000 per degree centigrade, so that
temperature variations will cause the delay time to drift. This can be
compensated for by providing a trigger generator whose PRF is altered
to take account of changes in the delay time. A simple way of doing this
is to use another supersonic delay line as the timing element in the trigger

Fig. 16-12.—Trigger generator.

generator, as shown in Fig. 1612. The circuit works as follows. When
the blocking oscillator fires, it delivers a trigger to the system and also
shock-excites a 15-Mc/sec resonant circuit. The oscillations so set up
are passed through the delay line, and thereafter amplified and detected.
The delayed signal is used as a trigger; it is applied to the blocking oscil¬
lator, which then fires and starts a new cycle. By making one of the
delay lines variable in length (which requires a different design from that
of Fig. 1610) the delays in the trigger and signal circuits can be matched

Sec. 16-4] ALTERNATIVE METHODS FOR OBTAINING COHERENCE 635

initially. The two lines are mounted close together in a thermally
insulated box so that the temperature changes equally for both.

164. Alternative Methods for Obtaining Coherence. —Figures 16-6
and 16-9 show two different ways of producing coherence between echo
signals and a reference signal: in the first method, the oscillator whose
phase is locked runs at radio frequency and the signals are added at
radio frequency; in the second, the locking and adding are both done at
the intermediate frequency.

Fig. 16-13.—-I-f locking, i-f addition., (a) I-f Locking by", transmitter, -f addition.

(6) I-f locking by oscillator, i-f addition.

It is also possible to lock at radio frequency and add at intermediate
frequency. Further, the oscillator can be made to lock the phase of the
transmitter instead of vice versa. The various arrangements can
therefore be classified according to—

1. Whether the transmitter locks the oscillator or vice versa.

2. Whether the locking takes place at radio frequency or intermediate
frequency.

3. Whether the signals are added at radio frequency or intermediate
frequency.

636

MOVING-TARGET INDICATION

[Sec. 16-4

(a) (f>)

Fig. 1614.—R-f locking, r-f addition, (o) R-f locking by transmitter, r-f addition.
(b) R-f locking by oscillator, r-f addition.

(o) (6)

Fiq. 1615.—R-f locking, i-f addition, (a) R-f locking by transmitter, i-f addition,
(b) R-f locking by oscillator, i-f addition.

Sec. 16-4] ALTERNATIVE METHODS FOR OBT AINING COHERENCE 637

Taking all possible combinations, we get 2 3 different types of circuit.
These are shown in Figs. 16-13 to 16-16.

The circuit shown in Fig. 1613a has advantages over the other
schemes. In the first place, the signals are added at intermediate

(<■)

(f>)

Fig. 16-16.—I-f locking, r-f addition, (o) I-f locking by transmitter, r-f addition.
(6) I-f locking by oscillator, r-f addition.

frequency, which allows amplification of the signals before addition.
Second, i-f locking is superior to r-f locking. The latter is hard to do in
the case of the transmitter, because of the large amount of power required;

638

MOVING-TARGET INDICATION

[Sec. 16-5

it is also difficult if the stable r-f oscillator is to be locked, because of the
high Q required to make the oscillator stable. Locking a coherent i-f
oscillator is easy since the Q can be smaller by a factor of 100 for the
same allowed rate of frequency change. The scheme of Fig. 16T36,
which uses i-f locking and i-f adding, is inconvenient because it requires a
power amplifier.

PERFORMANCE CRITERIA AND CHOICE OF SYSTEM CONSTANTS

The primary objective of moving-target indication is, of course, to
attain a high degree of discrimination in favor of the echoes from moving
targets compared to those from fixed ones. In order that this be accom¬
plished it is necessary that echoes, or clutter, from fixed targets be
eliminated or greatly reduced and that those from moving targets be
retained with optimum sensitivity compared to the residual clutter and
the inherent noise of the receiver.

Since the recognition of moving targets is based upon changes in the
returning echo from one pulse to the next, any changes present in the
signals from the fixed echoes will interfere with their elimination. Such
undesirable variations are of two sorts: (1) those inherently present in the
returning echoes, principally due to internal motions of the targets
themselves or to the effects of scanning; (2) spurious variations due to
instabilities or other shortcomings of the radar equipment. The methods
used and the constants chosen for the set should be selected in such a
way as to minimize the effects of the inherent fluctuations. The elimina¬
tion of spurious variations is largely a matter of careful engineering design.

Another factor to be considered in the choice of system parameters is
that since different radial velocities produce different changes in relative
phase from pulse to pulse, certain velocity intervals are much more
effective than others in producing large uncanceled signals. Indeed, a
phase change of one cycle—that is, a radial motion of one-half wavelength
between pulses—is equivalent to no change at all. Thus there are certain
“blind” velocity intervals in which the mass motion of the target does
not lead to a discernible indication. Since the velocities about which
these intervals are centered are determined by the wavelength and the
pulse repetition rate of the set, it is possible, within limits, to arrange that
they fall as little as possible in the range of velocities to be expected for the
targets of interest.

The various factors dealing with clutter elimination and target
visibility on a fixed system will be discussed in detail from both the theo¬
retical and the practical standpoint in the next few sections. The addi¬
tional factors present when the system is moving will be introduced later.

16-6. Stability Requirements. Frequency of the Beating Oscillators .—
The amplitude of the video signal from a stationary target can be written

Sec, 16-5]

STABILITY REQUIREMENTS

639

y = y 0 cos <f>, (1)

where y 0 is the i-f amplitude and <p is the phase difference between the
i-f echo signal and the reference signal. Now <p depends, as we have
already seen, only on the number of cycles executed by the stable local
oscillator and the coherent oscillator during the echo-time t j. Thus

4 > = (w; ± u t )h,

where ui and u c are the angular frequencies of the stable local oscillator
and the coherent oscillator, respectively. The positive sign is to be
taken when the local oscillator is tuned below the magnetron frequency,
the negative sign when it is above. If either oscillator varies in frequency
between pulses by an amount Aw, the phase change produced is then

A <p — h Au>.

If the frequency drifts at a uniform rate, then

“- T r

where T is the repetition period. Thus

A* - Th (2)

Now, from Eq. (1), we obtain, for the fractional change in beat amplitude,

— = — sin <p Aip,

V o

which has a maximum value equal to A <p. For a high-performance
MTI system a value of 6 per cent for A y/y 0 could be tolerated since this
represents the maximum residue of clutter amplitude left after can¬
cellation. The average residue will then be considerably less than 6 per
cent. The corresponding value of A<p is 0.06 radian or ywu cycle. On
substituting this value in Eq. (2) we get for the allowable rate of drift of
frequency

d l = __L_. (3)

dt 100 Tii w

For example, this has the value 20 kc/sec 2 for T = 1000 /nsec (PRF of
1000) and ti = 500 Msec (target at range of 50 miles). It will be seen
later that such a low rate of drift cannot be obtained in a local oscillator
without some special means of stabilization. In the case of the coherent
oscillator, on the other hand, the figure is readily attainable with a well-
constructed oscillator circuit.

640

MOVING-TARGET INDICATION

[Sec. 16-5

So far we have assumed that the coherent oscillator is exactly in tune
with the i-f echo signals. If this is not so, the video signals are no longer
square pulses but contain a number of cycles of the beat frequency, as
shown in Fig. 16-17. In the case of a moving target the beat cycles shift
horizontally from pulse to pulse and give a filled-in appearance on the
A-scope. Figure 16176 really represents coherent i-f rather than
coherent video signals, with the coherent oscillator acting as a second
local oscillator. Thus a loss in signal-to-noise ratio occurs when the
signals are passed through the video amplifier, whose bandpass character¬
istic is wrong for i-f signals. It is interesting to note that a gain in signal-
to-noise ratio can be obtained theoretically by detuning the coherent

oscillator sufficiently and replacing

(a) \-r-m- _ the video amplifier by an i-f ampli-

fier having a suitable pass band. 1
However, since this scheme requires
w— V\j -JIT-A—y/lP— much greater precision in the cancel¬

lation circuits, it is probably better to
retain the video amplifier and make
sure that the coherent oscillator is
always well tuned to the i-f signals. No serious loss in signal-to-noise will
occur if there is less than one-quarter of a beat cycle in each pulse. This
means, for example, that the detuning should be less than 1 Mc/sec in the
case of a I-psec pulse.

Magnetron Frequency .—The frequency stability required of the magne¬
tron can now be considered. The effect of a change Af m is to alter the
number of beat cycles within the “video” pulse by the amount t Af m ,
where r is the pulse length. For reasons similar to those used in con¬
nection with the beating oscillators, this quantity should not exceed
cycle from pulse to pulse. Hence we get for the allowed rate of drift, in
the same way as before,

df m = 1

dt lOOTY

Fig. 16-17.—Effect of detuning the
coherent oscillator, (o) Oscillator in tune
with i-f signals. (6) Oscillator detuned.

(4)

For T = 1000 Msec and r = 1 Msec, the rate is 10 Mc/sec 2 , which is 500
times the permissible rate for the beating oscillators. We conclude that,
if it is found necessary to have AFC on a system with MTI, it should be
applied to the magnetron rather than the local oscillator.

Variation in magnetron frequency from pulse to pulse causes another
kind of effect in the case of extended ground clutter. Consider two clutter
signals that just overlap in range. If the magnetron frequency changes
by an amount Af m , there will be a relative phase shift between the two
echoes which amounts to r A f m cycles. This phase shift will cause the

1 A. G. Emslie, “MTI Using Coherent IF,” RL Group Report No. 104—8/22/45.

Sec. 16-5]

STABILITY REQUIREMENTS

641

echoes to beat in amplitude in the region of overlap, even when no coher¬
ent reference signal is present. Since the expression for the phase shift is
identical with the previous expression, Eq. (4) also applies here.

Extra cycles will also appear in the video pulses if the magnetron fre¬
quency varies during the transmitted pulse. Such variation occurs
chiefly at the beginning and end of the pulse. If A/i is the maximum
departure in frequency from the value in the central part of the pulse,
the number of beat cycles is certainly less than r A/i. With the same
criterion as before we therefore should have

r 4f> < - (5)

For a 1-Msec pulse this gives A/i < j Mc/sec. However, since most of the
effect is concentrated near the ends of the pulse, a much larger variation
is probably permissible. Since the frequency pattern within the pulse
does not change from pulse to pulse, the quality of the cancellation is not
affected. All that is involved is a slight loss in signal-to-noise ratio for
moving targets.

Cancellation Equipment .—Consider next the stability requirements on
the cancellation equipment. The detectability of a signal on the PPI can
be roughly measured by the area under the voltage pulse. Thus if the
trigger and signal delay lines differ in delay time by an amount An, there
will be two uncanceled spikes of width An for each echo. In order to
cancel, for example, to 4 per cent, we must therefore make An less than
2 per cent of the pulse length. The delay lines should be capable of
matching each other within this tolerance for at least an hour at a time.
Likewise the amplitudes of the signals in the delayed and undelayed
channels should match to 4 per cent for an hour at a time.

Modulator. —Pulse-to-pulse variation in the repetition rate can pro¬
duce the same effect as unmatched delay lines. Thus the modulator
should fire relative to the trigger with a variation of not more than 2 per
cent of the pulse length, or - 5 V Msec in the case of a 1 -Msec pulse.

Finally, we have to consider the effect of variation in pulse length. If
this should change by an amount At from one pulse to the next, there will
be an uncanceled spike of width At. Thus we should not allow At/t to
exceed 4 per cent.

Variation in pulse length can also cause an indirect effect on the phase
of the coherent oscillator when the latter is not in tune with the i-f echo
signals. Let us assume, for example, that the locking pulse causes the
coherent oscillator to execute forced vibrations at the intermediate fre¬
quency for the duration of the pulse, after which it reverts to its natural
frequency. Then the variation in phase of the coherent oscillator is given
by At • A/ (in cycles), where A / is the amount by which the coherent

642

MOVING-TARGET INDICATION

[Sec. 16-6

oscillator is off-tune. Taking At = 0.04 jusec (for r = 1 msec) and allow¬
ing a phase change of ttjIj cycle, we get A f = \ Mc/sec.

Summary of Requirements .—Table 16.1 summarizes the stability
requirements. It should be mentioned that these figures represent almost
ideal conditions, in which the clutter to be canceled shows no fluctuations
of its own. If for any reason (such as rapid scanning rate) the clutter
should fluctuate by 10 or 15 per cent from pulse to pulse, there would be
no sense in canceling to 3 or 4 per cent. In such a case, some of the require¬
ments in the table could be relaxed considerably.

Table 161.— Stability Requirements for High-performance System with
PRF of 1000 pps, Pulse Length 1 msec, Ground Clutter out to 50 Miles

Component

Quantity

Maximum allowable value

Stable local oscillator.

Frequency drift

20 kc/sec 2

Coherent oscillator.

Frequency drift

20 kc/sec 2

Magnetron. r .

Frequency drift

10 Mc/sec 2

Magnetron.

Frequency change within

I Mc/sec 2 (and probably

pulse

much more)

Modulator and magnetron.

Pulse length variation from
pulse to pulse

Coherent oscillator.

Detuning from intermedi¬
ate frequency

i Mc/sec

Modulator.

Stability relative to trigger

tV Msec

Delay lines.. . . . 1

Relative drift in delay time

4 Msec/hr

16-6. Internal Clutter Fluctuations. —In this section we shall consider
echo fluctuations due to internal motions of the clutter—for example, the

motions of trees in the case of ground
clutter. The ground-clutter pattern
may include strong echoes from sin¬
gle targets, especially in regions
where t)iere are large structures hav¬
ing simple geometrical shapes.
Echoes from water towers and build¬
ing faces may easily equal in inten¬
sity the composite echo obtained
from a mountainside. However,
echoes from structures are generally
found to be fairly steady since the
targets do not sway much in the wind
and do not present a serious cancellation problem when the antenna is
stationary.

Most ground clutter is composite in the sense that the echo amplitude
at a given instant is the vector sum of many small echoes from the indi¬
vidual targets scattered over a land area determined by the beamwidth

(a)

Fig. 16-18.—Composite nature of
ground clutter, (a) Illuminated area of
clutter. (6) Contributions to signal: fixed
clutter = J2i; moving clutter = R 2 ; result¬
ant signal = R; resultant for next pulse =
R'\ variation between pulses = r.

Sec. 16-6]

INTERNAL CLUTTER FLUCTUATIONS

643

and half the pulse length, as shown in Fig. 16 18a. The individual
targets may consist of rocks, tree trunks, tree branches, leaves, etc.
Some of these, such as the rocks, are fixed. Others, such as the branches
and leaves, move in the wind. In Fig. 16- 18fo, the vector 7i, represents
the contribution from the fixed targets and 70 that from the moving
targets, and R is the resultant signal. At the next pulse, 7? 2 changes to
R'i, and the resultant to R'. The small vector r is the pulse-to-pulse
change.

Individual moving targets in the illuminated area are so numerous
that even the largest is small in size compared with their sum. Also the
phases of their echo signals are completely independent. Under these
two conditions, the vector 70 has a probability distribution like that of
statistical noise—that is, the end of the vector has a Gaussian distribution
about the point O'. The pulse-to-pulse change r likewise has a Gaussian
distribution.

The final result connecting r and 7f 2 is the following:

(r )rma

(6)

where f, is the PRF, X the wavelength, and k a factor that depends on the
wind speed and type of terrain. Measurements of the ratio of (r)™, to
(77)™. have been made by H. Goldstein. 1 The following table gives
typical values extrapolated from the experimental figures which were
obtained using a repetition rate of 333/sec. The voltage ratio of fixed to
variable clutter is also given. In the case of sea and storm echoes, there
is no fixed component.

Table 16 2.—Typical Measured Values op Clutter Fluctuation

Kind of clutter

Voltage ratio of rms
fixed component to
rms variable com¬
ponent

1 Total echo/rms fluctuation,

| db

PRF = 500

1000

2000

Thunderstorm.

9.2

Sea echo..

9 2

Sea echo.

Wooded terrain (wind

3.2

45 mph).

Wooded terrain (wind

3.2

25 mph).

Wooded terrain (wind

3.2

«1.

25 mph). 1

Wooded terrain (wind

9.2

0 9

10 mph).

9.2

3.7

1 Secs. 613 to 6 21 of Vol. 13 of this series.

644

MOVING-TARGET INDICATION

[Sec. 16-7

Several remarks are in order regarding the generality of the above
experimental values. Both the amplitude and the velocity of sea clutter
can be expected to vary widely with weather. Storm echoes are variable
in character, depending perhaps upon their internal turbulence. A reduc¬
tion of storm echoes by 10 db or more has been frequently observed on a
10-cm MTI system at 2000 pps. On some occasions, however, the reduc¬
tion of echoes from certain areas of the storm has been negligible despite
a tangential wind velocity.

The wooded terrain is that of New England in summer. Limited
evidence suggests that there is little change with the seasons. However,
some questions of importance remain with regard to ground clutter.
On the PPI of a 10-cm MTI system operating near Boston at a PRF of
300, many thousands of uncanceled targets have been observed under
conditions that make an explanation difficult. These targets, which
might possibly be birds, have been noticed to increase in number just
after sunset.

When extrapolating to other wavelengths, it should be borne in mind
that the wavelength dependence of Eq. (6) cannot be expected to hold
rigorously. Classes of moving reflectors that are negligible at 10 cm may
become of importance at 3 cm.

Fig. 16-19.—Scanning fluctuations of the echo from an isolated target, (a) Linear
receiver, (b) Limiting receiver.

16-7. Fluctuations Due to Scanning. —When the radar beam sweeps
over a simple isolated target, the received echoes vary from pulse to pulse
as shown in Fig. 1619a. The envelope of the echoes is the antenna pat¬
tern (voltage two ways), and the maximum pulse-to-pulse variation Ay
occurs at the point where the antenna pattern has its maximum slope.
Thus Ay can be readily calculated if a Gaussian error curve is used as an
approximation to the actual antenna curve. The result can be written in
the form

where y 0 is the maximum received voltage and n is the number of pulses
transmitted while the antenna rotates through an angle equal to the

Sec. 16-7]

FLUCTUATIONS DUE TO SCANNING

645

beamwidth (as measured between half-power points, one way). For
example, in the case of a 1° beam rotating at 6 rpm with a PRF of 1000, n
is 28 and Ay is therefore 5 per cent of y 0 . This represents the residue that
would be left after cancellation if a linear receiver were used.

In the next section it will be shown that a nonlinear receiver is neces¬
sary in order to remove all the clutter from the PPL Figure 16-196
shows the output of a simple limiting receiver; the maximum pulse-to-
pulse variation Ay i is less than before and occurs farther out on the
antenna pattern. The fluctuation is now given by the expression

Ay, _ k
Vi n

( 8 )

where k is no longer a constant but depends on the ratio of maximum input
signal i/o to the limit level y,, as shown in Table 16-3.

Table 16-3

y i

5.1

100

7.2

1000

8.7

It will be noticed that k does not change much as the input signal strength
is varied over a wide range. This makes it easy to obtain removal of
clutter of varying size.

Now let us consider the fluctuations in the
case of extended ground clutter. The echo
from such clutter, as we have already seen in
Sec. 16-6, consists of the vector sum of the con¬
tributions of a large number of scattering ele¬
ments. As the beam sweeps over the ground,
new elements are illuminated and the old ones
pass out of the beam. Thus the signal fluctu¬
ates in both amplitude and phase, as shown in
Fig. 16-20, where R is the signal voltage at a
given instant and R' the value after one repeti¬
tion period. The change from pulse to pulse is
represented by the vector r. If it is assumed that the scattering elements
are equal in size and randomly distributed, it is not hard 1 to calculate the
ratio of the rms values of R and r. The result is

r e (f[/Wde) h

ir-n 7 - ' ®

( J lf(0)]*de)

1 A. G. Emslie, “Moving Target Indication on MEW,” RL Report No. 1080,
Feb. 19, 1946.

an extended target.

646

MOVING-TARGET INDICATION

[Sec. 16-8

where r 0 and Ra are the rms values of r and R, 0 is the beamwidth, n is
the number of pulses per beamwidth, and f(6) is the antenna pattern
(voltage two ways). For the case of a Gaussian antenna pattern, we
obtain the equation

r« _ 1.66
Ro n

( 10 )

It is convenient to analyze the fluctuation into an amplitude part and
a phase part. To do this we can resolve the vector r into two components,
one in the direction of R, the other at right angles to R. The rms value
of each of these components is r 0 /-\/2. Thus the rms fluctuation in
amplitude is r 0 /V2 and the rms fluctuation in phase is approximately
r 0 /(R 0 \/2). We can therefore write

Rms pulse-to-pulse amplitude fluctuation
Rms pulse-to-pulse phase fluctuation

1.66

-75

n \/2

1.66

-— radians.

nV 2

(ID

These equations apply to the case of uniformly distributed scattering
elements. It might appear that a sudden discontinuity in the density
of scattering elements would cause a larger fluctuation. To see that this
is not so we can consider the integral (/[/'(fl)] 2 which is proportional
to the rms pulse-to-pulse fluctuation r 0 . In the case of a uniform distribu¬
tion of scattering elements, the limits of integration are from — » to + «.
When there is a discontinuity at an angle Oi from the center of the beam,
the limits are 9i to », and the integral will be less than before since the
integrand is everywhere positive.

16-8. Receiver Characteristics.— Ideally, an MTI system would
remove all clutter signals from the scope, maintaining the greatest possi¬
ble sensitivity for moving targets both in the clear and in the clutter.
Practically, this is not always possible, because of clutter fluctuations,
the finite perfection of cancellation, etc. Under these circumstances, it
appears desirable to adjust the residual clutter, after cancellation, so that
it resembles receiver noise in amplitude and texture when it is presented
on the scope.

Clutter fluctuations already have an amplitude distribution like that
of noise, whether they are due to scanning or to the action of the wind.
Thus the only problem left is to reduce the rms fluctuation to the same
value everywhere. There are two ways of doing this, the first depending
on the nature of the amplitude fluctuations of the clutter, the second on
the nature of the phase fluctuations.

As we have seen, the rms fluctuation in amplitude is proportional
to the rms clutter amplitude. Thus if x is the size of the clutter at the

Sec. 16-8] RECEIVER CHARACTERISTICS 647

input of the receiver, the total increment in amplitude can be written as

Ax = kx + N,

where kx is the amplitude component of the clutter fluctuation and N is
the component of the i-f noise vector in the direction of x. The output
fluctuation Ay is given by

Ay = | Ax,

and we require it to be independent of the clutter amplitude x. Thus we
have

dy K
dx kx + N’

where K is the (constant) value of Ay. Integrating this equation with the
condition that y = 0 when x — 0, we get the following expression for the
characteristic of the i-f amplifier:

+ < 12 >

For values of x giving a fluctuation kx considerably less than noise, the
characteristic is linear. For large values of x it is logarithmic. A
receiver with this characteristic is called a lin-log receiver.

The output of the lin-log i-f amplifier has to be added to the reference
signal and then detected. Since the clutter varies in phase as well as
amplitude, its phase variations are converted by the detector, when the
reference signal is present, into amplitude variations, which unfortunately
are not independent of the size of the clutter. It can be shown, however,
that no serious harm results if the reference signal level is kept somewhat
smaller than the maximum amplitude of the linear portion of the receiver
characteristic.

The second method of obtaining uniform output fluctuations depends
on the fact that the rms phase variation of the clutter is independent of
the size of the clutter. Thus all that is. required is a limiting i-f amplifier
to remove the amplitude variations, followed by a phase-sensitive detector
to convert the phase variations into uniform amplitude variations. To
obtain the maximum sensitivity for targets moving in the clutter it is
necessary that the phase-sensitive detector should have a linear character¬
istic—that is, the output amplitude variation should be proportional to
the input phase variation. This can be achieved by using a balanced
detector for mixing the reference signal with the output of the limiting
i-f amplifier.

The relative advantages of the two types of receiver will now' be
considered. If the lin-log receiver is used, it is possible to dispense with

648

MOVING- TA RGET INDICA TION

[Sec. 16-8

the oscillator and amplifier shown in Fig. 16-11 and to send the i-f signal,
together with the reference signal, directly through the delay line. The
amplifier then works at the intermediate frequency used in the receiver.
These changes make the circuit simpler and avoid the problems of carrier
modulation and demodulation. However, the loss of freedom in the
choice of frequency for the delay line and the comparison amplifier is a
disadvantage. Also, the method is not suitable for “ back-of-dish ” radar
sets, since the i-f signals cannot conveniently be brought out through
slip rings. This method of using a lin-log receiver should be used only
when simplicity and compactness are of prime importance. In general,
such a receiver should be used in conjunction with an oscillator and
amplifier (Fig. 16-11) in the usual way.

An important advantage of the limiting receiver is that the output
video signals have a range of amplitude extending from noise only up to
the limit level. This small dynamic range makes it easy to design the
cancellation circuits. For the lin-log receiver, the dynamic range is 6 to
12 db greater under conditions of equal performance.

For general MTI use, the limiting type of receiver is to be preferred.
However, there is a type of MTI system in which moving targets are
detected in the clutter by the fluctuations which they produce in the
clutter amplitude. The lin-log receiver must be used in such a system,
since the limiting receiver cannot detect amplitude changes.

Some idea of the magnitudes involved in the receiver problem can be
obtained from Table 16-4. The fluctuations due to the wind were

Table 16-4.—Fluctuations Due to Wind and Scanning

Beam-

Scanning

Pulses per

Wind effect

Scanning effect

PRF

width,

rate,

beam-

rms flufctuation

rms fluctuation

degrees

rpm

width

rms total echo

rms total echo ’

9.2

500

-34

-22

9.2

2000

250

-46

-44

obtained from Table 16-2 for wooded terrain and a wind velocity of
25 mph. The scanning effect was derived from the formula for extended
clutter in Sec. 16-7. It will be noticed that the scanning effect predomi¬
nates in the case of the low PRF and narrow beam, whereas the two
effects are about equal for the high PRF and wide beam. The fluctua¬
tions in the first case are roughly 10 per cent, considerably greater than
the fluctuations due to instability of the components. On the other
hand, the fluctuations in the second case are only about 1 per cent and are
therefore negligible compared with system instability.

Sec., 16-91

TARGET VISIBILITY

649

Consider how a limiting receiver should be adjusted in each of these
cases. Since only the phase part of the fluctuation is selected, the fluctua¬
tion of the video output is 1/ y/2 or 3 db less than the total input fluctua¬
tion. Thus the figure — 22 db becomes —25 db at the output, which
means that the rms fluctuation in the first case is about xj of the limit
level. Therefore, in order to obtain a PPI with uniform background, the
gain control of the receiver, ahead of the limiting stages, should be
adjusted so that rms noise is also ^ of limit level. “Peak” noise is
then about l of limit level. This adjustment of noise relative to limit
level is made while viewing the output of the limiting receiver on an
A-scope. When this has been done, the video gain control is adjusted
so that the noise and canceled residue just show on the PPI. The MTI
photograph in Fig. 16T shows everything in correct adjustment so that
the residue of the clutter blends with the noise. The corresponding
photograph in Fig. 16-2 shows a case of incorrect adjustment: receiver
noise is too large compared with the limit level. The result is that the
residue does not show on the scope and black “holes” appear where the
clutter was. Under these conditions there is an excessive loss of sensi¬
tivity for moving targets in the clutter.

In the second case (high PRF and broad beam) the predominating
fluctuations will be due to system instability and may be of the order of 5
per cent (peak) if all the stability requirements are met. Thus peak
receiver noise should in this case be set at 5 per cent of limit level.

16-9. Target Visibility.—There are two problems to be discussed in
this section. The first has to do with the visibility of moving targets
when they are clear of the clutter; it includes consideration of undesirable
targets, like clouds, as well as desirable targets such as aircraft. The
second problem is concerned with the visibility of moving targets that
occur at the same range and azimuth as ground clutter.

Targets in the Clear .—We have seen in Sec. 16-2 that the video pulses
from the MTI receiver, in the case of a moving target, are amplitude-
modulated at the doppler frequency f.i. Thus the pulse amplitude at a
given instant t is given by

V i = y n COS 2-rrfdt.

For the next pulse,

2/2 = 2/o cos 2ir f d (t + T).

The canceled video pulse is therefore

V = 2/i - 2/2 = 2i/o sin (irf/f ) sin 2irfd (t + (13;

Thus the canceled pulses also exhibit the doppler modulation frequency
and have an amplitude

y' 0 = 2y 0 sin (tt f d T).

(14)

MOVING-TARGET INDICATION

650

[Sec. 16-9

This expression is zero when f d is a multiple of the PRF and, since
fd = 2v/X, the first “blind” speed is given by

2 Vl T

= 1,

2 ’

(15)

where f, is the PRF. In other words, the target appears to be at rest
when it travels a distance X/2 (or a multiple of X/2) between pulses.
Numerically,

First blind speed = X/ r /89 (X in cm, speed in mph) (16)

Going back to Eq. (13) we see that the average canceled signal, after
rectification, is given by

]y\ = -J/oisin (icfdT)\. (17)

We have to compare this amplitude with that of noise after cancellation.
The noise amplitude in the delayed channel is completely independent of
that in the undelayed channel. We must therefore add the noise powers
in the two channels, obtaining an increase of y/2 in noise amplitude after
cancellation. Hence the change in signal-to-noise ratio caused by the

addition of MTI is represented by
the factor

[ 1 . 0 '
I 0.5

Radial velocity of target

7T \/2

|sin (t fdT)\.

(18)

Fig. 16-21.—Response curve for target

in the clear. The first blind speed has the TnC numerical factor is flbout 0.9.
value \/r/89 (X m cm, speed m mph). Thus MTI causes scarcely any loss

for a target moving at the optimum speed but does cause a loss at other
speeds. Figure 16-21 shows the voltage response for MTI relative to the
response for a normal radar set.

It will be observed that the response at small speeds is proportional
to the speed v. It can be written as follows:

Response
Max. response

( 20 )

where tq is the first blind speed. As an example, consider a set with
X = 9.2 cm and/. = 2000 pps. Then from Eq. (16) we have iq = 206 mph.
For a storm cloud traveling radially at 30 mph, the ratio in Eq. (20)
becomes 1/2.2 or —7 db, whereas Table 16-2 shows that the fluctuation due
to internal motion of the cloud is only —17 db. From the MTI point of

Sec. 16-9]

TARGET VISIBILITY

651

view translational motion is more serious than the internal motion of the
cloud. It should be noticed that the two effects change together as the
PRF is varied.

A question of some interest is the following: If a target of given size
can have any radial speed with equal probability, how often will it be
detected? Let us suppose that the target, when moving at one of the
optimum speeds in Fig. 16.21, gives a signal N times as large as the mini¬
mum detectable signal. Then the relative response at other speeds is
given by

N sin (it fdT).

The target will be seen as long as this quantity is greater than unity; the
probability of this being the case is

7T
2

( 21 )

Normal

Fig. 16-22. —Probability of seeing a
moving target.

Fig. 16-23. —Moving target in clut¬
ter: clutter = R‘, target = s; target at
next pulse = s'; variation between
pulses = r.

A plot of this expression is shown in Fig. 16-22. The probability is 0.5
when N = \/2; consequently in this sense we can say that MTI causes
an average loss of y/2 in voltage or 3 db. 1

Targets in the Clutter .—We have seen in Secs. 16-6 and 16-7 that the
fluctuations of extended clutter, whether due to the wind or to scanning,
have noiselike character. This “clutter-noise” is what appears on the
MTI scope at places normally occupied by the clutter, and it is adjusted
to be equal in brightness to ordinary noise. A moving target in the

1 The above discussion neglects the fact that the phase-sensitive detector reduces
the noise voltage by i/2- Thus Eq. (18) should be multiplied by \/2, as should
the ordinate of Fig. 16.21. The abscissa of the MTI curve of Fig. 16.22 should be
divided by \/2 . Use of MTI may thus entail no average loss.

652

MOVING-TARGET INDICATION

[Sec 16-9

clutter has to compete with the clutter-noise in much the same way as a
target in the clear competes with ordinary receiver noise. Figure 16-23 is
a vector diagram for a moving target in the clutter. The pulse-to-pulse
variation r in the resultant vector has both amplitude and phase com¬
ponents just like the clutter fluctuations. The magnitude of r can easily
be obtained from the fact that $ rotates with the doppler frequency f,i.
Thus the angle between .s and s' is 2irf d T, and accordingly

r = 2s sin (tt f d T). (22)

This equation, which is the same as Eq. (14), shows that blind speeds
also exist for targets in the clutter. If we take the arithmetical average
of Eq. (22) for all speeds, we get

r —

(23 a)

If, on the other hand, we take the median with respect to velocity, which
is the average that we took in the case of targets in the clear, we get

f = y/2 s. (23b)

Since the two values of f differ by only 10 per cent or about 1 db, it does
not matter which we take. The value given by Eq. (23a) is also the
arithmetical average for the case of a noncoherent signal from a signal
generator. Measurements can therefore be made without appreciable
error by using the signal from a signal generator instead of that due to an
actual target.

A moving-target or signal-generator pip can be expected to be visible
on the PPI if f is at least three times the rms clutter fluctuation r 0 .
Using Eq. (23a), this condition can therefore be written as

s = ^ r 0 = 2.4r 0 . (24)

That is, the signal amplitude should be 8 db larger than the rms clutter
fluctuation.

It is convenient to express the visibility condition in terms of the rms
clutter amplitude R<t instead of the rms fluctuation. In the case of
scanning effects this leads, with the help of Eq. (10), to the following sim¬
ple relationship:

— = j (scanning), (25)

S 4

where n is the number of pulses per beamwidth. In the case of wind
effects, we have, from Eq. (6),

X/ r (wind).

(26)

Sec. 16-10]

CHOICE OF SYSTEM CONSTANTS

C53

As is pointed out at the end of Sec. 16-6, the dependence on X is only
approximate.

The ratio R 0 /s, which can be called the “subclutter visibility,” gives
a measure of the performance of an MTI system. When scanning and
wind effects are present together, along with the effect of system instabil¬
ity, we have to go back to Eq. (24) and write it as

s = 2.4(r^ can „i„ e + + rS as , t . m )-% (27)

since the three fluctuations are independent of each other. Now each
fluctuation is proportional to the size of the clutter. Thus we have

Ro _ _J_

K\n- K\y-p r K\

where the terms in the denominator refer respectively to the effects of
scanning, wind, and system instability. The quantities K , and A" 2 are
constants, but K 3 may depend somewhat on X and / r . For example, it is
probably harder to stabilize the local oscillator at 3 cm than at 10 cm.
Again, Eq. (3) shows that the repetition rate enters into the stability
condition. However, we shall assume, for simplicity, that the over-all
system instability is independent of X and },.

16-10. Choice of System Constants. —The following are the objectives
in the design of a ground radar set with MTI:

1. Maximum sensitivity to moving targets in the clutter.

2. Maximum sensitivity to moving targets in the clear.

3. Maximum cancellation of undesirable moving objects, such as
clouds.

Some of these objectives are in direct conflict with the normal aims of
a radar set. For example, a broad beam and slow rate of scan will reduce
scanning fluctuations and therefore help the first objective, but will
decrease resolution and hamper the rate of flow of information. Because
of this, MTI should be integrated into the radar set from the start and
not added as an afterthought.

Subclutter Visibility. —From Eq. (28) we see that the subclutter
visibility can be increased by increasing n and X/ r , but that nothing much
is gained by going greatly beyond the point where the scanning and wind
fluctuations are equal to those due to system instability. A well-de¬
signed system might have an rms instability of 2 per cent, in which case,
from Eq. (24), the greatest possible subclutter visibility is 26 db. There
is then no need to make the individual subclutter visibilities for scanning
and wind greater than 30 db. For the case of scanning, that means, from
Eq. (25), that n does not have to be larger than 120 pulses per beamwidth.
Again, from Eq. (24), the rms wind fluctuation should be less than 22 db.
This happens to be the value for wooded terrain when X = 3.2 cm and

654

MOVING-TARGET INDICATION

[Sec. 1610

J r = 500 and the wind velocity is 25 mph, as is shown in Table 16-2.
Thus, X/ r should be about 1600 for this particular wind speed. In gen¬
eral, it is easy to obtain the required figure for X/,, but not for n, without
sacrifice elsewhere. Scanning fluctuations are the principal difficulty in
MTI design.

The quantity n is proportional to beamwidth and PRF, and inversely
proportional to scanning rate. It has the value 120 for a PRF of 720 with
a 1° beam rotating at 1 rpm. Although this set of constants satisfies the
condition above, the scanning rate is too slow for many purposes. To
attain greater rate without losing subclutter visibility, either the beam-
width or PRF must be raised; the alternative is to take a loss in subclutter

visibility, which may be the best solu¬
tion in some cases. For example, if the
targets are all larger than the clutter, a
subclutter visibility of zero db is suffi¬
cient. In that case the scanning rate can
be raised to 30 rpm. It is, therefore, of
considerable importance to use all possi¬
ble methods of decreasing the size of the
clutter relative to the moving targets,
such as shaping the beam in elevation,
using short pulses, and choosing the site
carefully.

Blind Speeds .—It has already been
seen that MTI causes an “average”
loss of about 3 db when all radial speeds
are equally probable. 1 This is true no
matter where the blind speeds happen
to fall. We are interested, however, in
targets such as airplanes and clouds which have non-uniform distributions
of radial speeds, and would like to know the best values of the blind
speeds in these cases.

Figure 16-24 shows the distribution of radial velocities for airplanes
whose ground speed can have any value between 100 and 400 mph with
equal probability and whose direction of flight is random. It is hard to
choose the best blind speeds from this graph. There will probably be
an average loss 1 of about 3 db, as in the case of a uniform distribution,
whether there are many blind speeds in the interval 0 to 400 mph or
whether the first optimum speed comes at, for example, 400 mph. The
choice of blind speeds is of no particular consequence, per se; but there
may be special cases, such as airport traffic control, where the radial speed
can be regulated. Blind speeds can then be chosen accordingly.

1 See footnote on p. 651.

Radial speed in mph

Fig. 16-24.—Distribution of radial
speeds for random aircraft, assuming
all ground speeds equally likely in
range 100 to 400 mph and all direc¬
tions equally likely.

Sec. 1611] COMPENSATION FOR VELOCITY OF SYSTEM 655

To get the greatest cancellation of an undesirable moving object, the
first blind speed, v lt should be made as large as possible. For example, if
i>i is 30 times the radial speed of the object the response will be 10 per cent
of the maximum value, by Eq. (20). In the case of clouds moving at
30 mph, that gives us i'i = 900 mph, which is a suitable value as far as
Fig. 16-24 is concerned. Since V\ = X/,/89, it can be seen that such a high
value of Vi is obtainable, when a normal PRF is used, only by going to a
wavelength of the order of 100 cm. For microwave frequencies, therefore,
one can scarcely reduce storm echoes by more than about 10 db.

In the detection of ships, whose velocities are comparable with those of
clouds, it might be thought that the ships would be canceled along with
the clouds. This is not so because ships, when within the horizon, give
much larger signals than clouds, and still show up strongly after a 10-db
cancellation.

MOVING-TARGET INDICATION ON A MOVING SYSTEM

1641. Compensation for Velocity of System. —Figure 16-25 shows
what has to be done to compensate for the velocity of the station when a
system is carried on a ship or airplane. The phase-shift unit shown in a
changes the phase of the reference signal at the same rate as that at which
the phase of fixed echoes is being changed by the motion of the station.
The effect is to give the station a virtual velocity which cancels the actual
velocity.

Figure 16-256 is a block diagram of the phase-shift unit. An oscillator
supplies a signal at the doppler frequency which is mixed with the refer¬
ence signal. The upper sideband is then selected by a crystal filter. The
addition of the doppler frequency to the reference signal is equivalent to
shifting the phase of the coherent oscillator at the rate of fd cps. It is to
be noted that this is not the same as merely tuning the coherent oscillator
to the frequency /„ + fd, since the phase shifter is applied after the oscil¬
lator is locked. Full details on the phase-shift unit can be found in a
report by V. A. Olson. 1

The doppler frequency depends on the radial component of velocity
and is therefore proportional to the cosine of the azimuth angle. It is
necessary to vary the frequency of the doppler oscillator automatically
as the antenna scans.

In an airborne set, there is a further complication due to the fact that
the radial velocity depends on the depression angle, which means that
the doppler frequency of the ground clutter varies with the range. In
consequence, the phase-shift unit cannot be used for clutter at large

1 V. A, Olson, “A Moving Coho Conversion Unit,” RL Report No. 975, Apr. 3,
1946.

656 MOVING-TARGET INDICATION [Sec. 1612

depression angles; some other method must be used, such as the nonco¬
herent method now to be described.

16-12. The Noncoherent Method. —We have already seen in Fig.
16-19 that a target moving in the clutter produces a resultant echo that
varies in both amplitude and phase. To detect the amplitude variations,
all that is required is a receiver that does not limit—that is, one with a
linear-logarithmic response. Since no coherent reference oscillator is
used, this is called the noncoherent method of detecting moving targets.
The ground clutter itself acts as the reference signal.

(b)

Fig. 16-25.—MTI on a moving system, (a) Block diagram of system showing location
of phase-shift unit, (b) Simplified block diagram of phase-shift unit.

In the noncoherent method the local oscillator does not have to be
stabilized since phase changes are not to be detected. However, the
transmitter must have the same stability as in the coherent method
because the overlapping ground clutter beats with itself if the transmitter
frequency varies from pulse to pulse. As shown in Table 16-1 the stabil¬
ity requirement is not at all severe.

Another great advantage of the noncoherent method is that it works
even when the radar set is carried on a moving station. This is because
the set is sensitive only to amplitude fluctuations, whereas the motion of
the station causes mainly phase changes in the received echoes. An
amplitude effect, due to the finite beamwidth, will be discussed later.

Sec. 1613 ] BEATING DUE TO FINITE PULSE PACKET

657

The simplest way of employing the noncoherent method is to use an
A-scope presentation and watch for echoes that are fuzzy on top. This
type of echo indicates the presence of a moving target in the clutter
at the range shown on the scope. The scheme is useful only when very
slow scanning can be tolerated. An alternative indication can be
obtained by gating off all but a short portion of the A-sweep and putting
the output through a pair of headphones. A moving target within the
“gate” then produces a musical note in the phones.

A more useful arrangement is to put the video output through the
usual cancellation circuits and display the moving targets on a PPI.
With such equipment in an airplane, roads will show up on the scope as
intersecting lines of dots due to the moving vehicles.

The drawback to the noncoherent method is that a moving target can
be detected only when there is ground clutter at the same range and
azimuth as the target. Thus although the method works well out to the
range where the clutter begins to get patchy, beyond this range moving
targets become lost in the clear places. A plan for overcoming this
difficulty is to have noncoherent operation for short ranges and coherent
operation for long ranges. This can be accomplished by gating off the
coherent reference oscillations for the required number of miles at the
start of each sweep. Since the station is moving, it is necessary, during
the coherent part of the sweep, to compensate for this motion. The
method of doing this has been described in the preceding section.

16-13. Beating Due to Finite Pulse Packet. —In addition to the
fluctuations due to scanning and wind, there is another kind of fluctuation
when the system is moving. This arises from the fact that the clutter
elements illuminated by the beam at a given instant do not, because of the
spread of radial velocities within the finite illuminated area, all have
the same doppler frequency. Signals from clutter will therefore beat
with each other at frequencies up to f x = 2 Av/\, where Av is the spread
in radial velocity.

Let v be the velocity of the system and 8 the azimuth angle. Then the
radial velocity is v cos 9, and thus we have

At; = — vQ sin 6 for 0 0,

where 9 is the beamwidth. If the beating is represented by a factor cos
(2tr/i<), then the fractional change in amplitude from pulse to pulse is of
the order 2x/i// r , which can be written as 4x Av/ (X/,) or 2x Av/v h where tq
is the first blind speed as defined in Sec. 16-9. For example, suppose

v = 300 mph, tq = 800 mph,

9 = 2° = radian, 9 = 90°.

Then Av — 10 mph and the fluctuation is 8 per cent.

658 MOVING-TARGET INDICATION [Sec. 16-14

When 0 = 0 the above equation for Av no longer holds and we have
instead

Av = -g-i>9 2 for 0 = 0.

For v = 300 mph and 0 O = -j'j radian, as before, we get Av = ^ mph,
showing that the fluctuations are negligible when the antenna is pointing
straight ahead.

When the system is carried in an airplane there is an effect due to the
depression angle as well as the azimuth effect just discussed. Since the
beam is usually broad in a vertical plane, the range of depression angles
within the illuminated area of clutter is limited by the pulse width.
Under these conditions the spread in radial velocity is given by

tv sin 3 4> cos 0
2 h cos 4>

for <t> « 90°,

where r is the pulse length (in feet), h the altitude, 4> the depression angle,
and 0 the azimuth. For r = 1000 ft (1 jusec), h = 10,000 ft, <f> = 45°,
0 = 0, v = 300 mph, we get Av = 8 mph, which is about the same as the
above value for the azimuth effect.

For very large depression angles, the formula becomes

Av = v <f> = 90°

For v = 300 mph, r = 1000 ft, h = 10.000 ft, we have Av = 100 mph,
illustrating that very large fluctuations are present in the clutter immedi¬
ately below the airplane.

COMPONENT DESIGN

The MTI systems designed at the Radiation Laboratory have been
at 10 and 3 cm. For that reason, the discussion of typical components
given here will be in microwave terms, despite the fact that MTI methods
are useful with radar systems operating at longer wavelength. The com¬
ponents that will be described have been chosen to illustrate recent devel¬
opments or the breadth of possibilities, or to supplement the detailed
treatment of the components elsewhere in the Radiation Laboratory
Series.

16-14. The Transmitter and Its Modulator. —The transmitter stability
requirements, specified in Sec. 16-5, can be met by magnetrons of existing
design. The 10-cm magnetrons that have been successfully tried for
MTI are the type 2J32, the type 4J47, and the type 700CY. At 3 cm,
the type 2.T42 has been used. Most experience available up to 1946 has
been with the 2J32. With the 2J32 and a hard-tube modulator, fre¬
quency modulation within a pulse never reaches an objectionable level

Sec. 16 - 15 ]

THE STABLE LOCAL OSCILLATOR

659

when amplitude modulation is avoided. Information on this point is not
available for the other types.

Magnetron frequency pulling with antenna scanning can be objection¬
able with any type of tube. It may be caused either by imperfect rotary
joints or by obstacles in front of the antenna. If the pulling is slow com¬
pared with 10 Mc/sec 2 (see Table 16-1), ground clutter will remain can¬
celed at all azimuths. However, when the absolute detuning becomes
excessive, moving targets will be lost owing to their high video spectrum,
as is explained in Sec. 16-5. This type of detuning is particularly
insidious.

Objectionable modulation of the transmitted pulse by the use of
60-cps power on the heater has been observed with the type 4J47. This is
probably caused by the magnetic field-of the heater current. No such
difficulty has been found with the 2J32, owing apparently to the design
and construction of the heater. Three methods of avoiding this modula¬
tion are available. At high PRF’s the heater current can be turned off
after starting the system, since the cathode temperature will be main¬
tained by bombardment. Alternatively the PRF can be made an exact
submultiple of the power-line frequency. Since neither of these methods
can be generally applied, it will sometimes be necessary to operate the
magnetron heater on direct current. Heater hum modulation should
eventually be made a matter of tube-manufacturing specification.

The use of a supersonic delay line necessitates a constancy of PRF to
yjj of a pulse width. This is the most severe new requirement placed by
MTI upon the modulator. It has been successfully met by hard-tube
and by hydrogen-thyratron designs. In their current state, triggered-
gap modulators were not quite adequate for MTI systems in 1946. Since
little effort had been put upon the jitter problem, it seemed reasonable to
expect that triggered gaps can be considerably improved. The rotary
gap can be used for MTI only if a storage tube serves as delay element.

16-15. The Stable Local Oscillator. —Two types of 10-cm local
oscillator tubes have been investigated: the type 417 and type 2K28
reflex klystrons. The 417 has a built-in cavity and is therefore more
microphonic than the 2K28, which has a demountable cavity. However,
the external cavity gives the 2K28 a lower Q, which causes larger noise
fluctuations and greater sensitivity to external 60-cps magnetic fields.
Both tubes show frequency modulation when the heaters are run on a-c
power.

The 2K28 was chosen for incorporation into the local oscillator unit
shown in Fig. 16-26. The outer metal case of this component is lined with
sound-proofing material. The parts within are mounted on a metal
base-plate which is in turn supported by four circular shear rubber shock
mounts of conventional design, not visible in the photograph.

660 MOVING-TARGET INDICATION [Sec. 1615

The oscillator tube is mounted, with its axis vertical, in a blackened
mu-metal shield visible to the left. A single pickup loop is connected to
two lines via a decoupling fitting. A tunable echo box (Johnson Service
Company Model TS-270/UP) is coupled to the oscillator by a rotatable

loop, the lever arm of which is visible close to the oscillator. An echo-
box crystal-current meter is of value in making tuning adjustments.

The remote power supply uses conventional electronic regulation. A
simple A (7-filter at the oscillator isolates the reflector electrode. Heater
power is furnished by a dry-disk rectifier and high-current filter.

The optimum value of echo-box coupling varies for different fre-

Sec. 1615]

THE STABLE LOCAL OSCILLATOR

661

quencies and different oscillators. If this coupling is too loose, frequency
instability will result. If the coupling is too tight, tuning will be difficult
and the power output from the local oscillator will be reduced. It must
be possible to obtain two to three times the mixer current that will
actually be used. When restarting a correctly tuned oscillator, it may be
necessary to vary the reflector voltage slightly up and down to cause the
echo box to lock in.

A microwave discriminator circuit developed by R. V. Pound 1 gives
promise of overcoming many of the difficulties of the simple echo-box
stabilizing arrangement. Measurements of local-oscillator stability at
3 cm, as reported below, show that this system of stabilization might be
adapted to MTI.

Table 16-5.— Typical Local-oscillator Stabilities

1 Described in detail in Chap. 2 of Vol. 11 of the series.

662 MOVING-TARGET INDICATION [Sec. 1616

Equation (3), giving the allowable rate of frequency drift in the local
oscillator, was based on the assumption that the frequency was changing
at a constant rate. Most frequency deviations are not of this simple sort.
They are more likely to be periodic or random, with a superimposed uni¬
form drift. The rate of change of frequency can be expressed by a
Fourier spectrum and the total phase error determined by superimposing
the contributions resulting from each of the Fourier components. These
components are not all equally harmful to MTI performance. A fre¬
quency modulation exactly synchronized with the PRF or any multiple
thereof would cause no MTI phase error whatsoever. The phase of
ground clutter at a particular range would be shifted by a given amount
from its value in the absence of the frequency modulation, but the shift
would be constant for successive transmitted pulses.

It has been shown 1 that the rate of change of oscillator frequency
averaged over all modulation frequencies can be used in place of the
simple df/dt of Eq. (3) as a figure of merit for local-oscillator stability.
Table 16-5 shows some typical figures on local-oscillator stability.

16-16. The Coherent Oscillator. —Locking at radio frequency has
been accomplished at 10 cm, but its feasibility for field service is yet to be
investigated. The relative ease and dependability of i-f locking have
resulted in its use for all coherent microwave systems of the past. This
section will discuss oscillators that receive an i-f locking pulse and deliver
an i-f reference signal according to the arrangement of Fig. 16-9.

The Locking Pulse .—If the phase-locking is to be constant from one
pulse to the next with a precision of 1°, the carrier-frequency packet that
does the locking must be unusually free of random components. These
may arise from several sources, of which the most likely is the transmit-
receive switch. The gaseous arc discharge in the TR tube generates noise¬
like oscillations. These may reach the coherent oscillator by passing
from the signal mixer, via the local oscillator, to the locking-pulse mixer.
The available remedies are the use of loose mixer coupling, lossy local-
oscillator cable, and separate pickup loops in the local-oscillator cavity.

Another cause of random components in the locking pulse is excessive
r-f pulse amplitude at the locking mixer. If the r-f pulse exceeds the
level of the local oscillator, self-rectification will take place, yielding a
video pulse that will have noncoherent components at the intermediate
frequency. Even though an effort has been made to reduce the r-f pulse
amplitude, this trouble may persist in a subtle form. If the attenuator
preceding the locking mixer is of the simple “ waveguide-beyond-cutoff ”
variety, it may allow harmonic frequencies, generated by the transmitter,

1 S. Roberts, “A Method of Rating the Stability of Oscillators for MTI,” RL
Report No. 819, Oct. 16, 1945.

Sec. 1616]

THE COHERENT OSCILLATOR

663

to pass to the mixer with so little loss that their amplitude is comparable
to or greater than that of the fundamental frequency.

A further source of locking trouble is statistical noise. If a simple
cable-coupling circuit is used in the absence of a locking-pulse preampli¬
fier, care must be taken to maintain adequate pulse amplitude.

Circuit Design .—Any conventional type of freely running oscillator
can be phase-locked by injecting into its tuned circuit a sufficiently large
carrier pulse. There is a certain degree of incompatibility between the
requirements that the oscillator be extremely stable and yet precisely
phasable. A simple method of reconciling these requirements is to stop
the oscillator completely before each radar transmission so that the lock¬
ing pulse is also a starting pulse. By this process, all previous phase
information is destroyed and the locking pulse is required to overwhelm
merely the statistical noise fluctuations present in the oscillator tuned
circuit. The stopping of the coherent oscillator can be accomplished by
applying a bias “gate” perhaps 100 nsec before each transmitted pulse.
This gate is released just before, during, or just after the locking pulse,
while the resonant circuit of the oscillator is still ringing. The amplifying
circuits that precede the oscillator can be made reasonably narrow since
pulse shape is unimportant. These circuits must be broad enough to
allow for local-oscillator detuning and to maintain a large locking-pulse-
to-noise ratio. It is advantageous to use a bias slightly beyond cutoff
in a late amplifying stage in order to suppress any spurious low-level
oscillations which, by their persistence, might introduce an appreciable
phase error either before or after locking. The actual injection of the
locking pulse into the oscillator might be accomplished in any of several
ways, including the use of an extra oscillator control grid. The most
flexible method and the one most widely used is the connection of the plate
of a pentode injection-tube across all, or part of, the LC-circuit of the
oscillator.

The oscillator itself must be designed with considerable care. The
resonant circuit must have a high Q. Input and output loading must be
held to a minimum. Heater hum modulation must be minimized by
keeping the d-c and r-f impedance between cathode and ground as small
as possible. The oscillator tube must be of a nonmicrophonic type. The
circuit as a whole must be rigidly constructed and shock-mounted.
Power-supply ripple must not exceed a few millivolts. When these
precautions are observed, free-running stabilities of around 1 kc/sec 2 can
be obtained at 30 Mc/sec. A typical oscillator with its preceding and
following stages is shown in Fig. 16-27.

Phase-shift Unit .—Figure 16-28 shows, in more detail than the simpli¬
fied diagram of Fig. 16-256, the arrangement of the phase-shift unit
required for MTI on a moving system. For station motion up to 400 mph,

664

MOVING-TARGET INDICATION

[Sec. 16-16

the doppler frequency at 10 cm will vary from plus to minus 3500 cps.
The way in which this frequency is added to the reference signal is shown
in the diagram. The doppler oscillator receives a shaft rotation and

delivers a linearly related frequency with an absolute accuracy of 2 cps.
This oscillator is similar to the General Radio Type 617-c Interpolation
Oscillator. The single sideband rejection requirements for the carrier
and unwanted sideband are very severe. The quartz filter was designed

Fig. 16-28.—Block diagram of a phase-shift unit.

by Bell Telephone Laboratories. Pending delivery of the latter, the
circuit was tested by means of LC-filters with one additional mixing
step, and found to cancel target motion satisfactorily. The absolute
accuracy of the circuit from the shaft of the doppler oscillator is about

Sec. 16-17]

THE RECEIVER

665

j mph at 10 cm. Full circuit information can be found in a report
by V. A. Olson. 1

16-17. The Receiver. —Two types of receiver characteristic have
been discussed in Sec. 16-8. The lin-log type is necessary in a noncoherent
system, and the limiting type is best for coherent systems.

The Lin-log Characteristic .—A linear-logarithmic characteristic is
linear for small signals and limits in a specified gradual fashion for large
signals. A method for achieving this response is shown in Fig. 16-29.
Output signals from several successive i-f stages are combined. At low
signal levels, the last stage delivers a linear signal in the normal fashion,
the output from the preceding stages being negligible. As the signal level
increases, the output signal of this last stage reaches a saturation level

Video output signal

Fia. 16-29.—Circuit to give lin-log response.

above which it cannot rise regardless of further input-signal increases.
At this point the output signal from the preceding stage has become
appreciable; it continues to increase with increasing input signal. Now,
however, the increase in output-signal level is at a slower rate because the
gain of the last stage is not available. Eventually the second stage
overloads and the third from the last becomes effective. The ampli¬
tude response curve of such a circuit can be adjusted to be accurately
linear-logarithmic. 2

The Limiting Receiver .—The block diagram of a typical limiting
receiver is shown in Fig. 16-30. The arrangement is one that might be
appropriate to a system employing a l-/asec pulse width and an inter¬
mediate frequency of 30 Mc/sec. The requirement that the amplitude
response show no inversion above the limit level is one not ordinarily met

1 V. A. Olson, “A Moving Coho Conversion Unit,” RL Report No. 975, Apr. 3,
1946.

* The design problems involved in this and other MTI receiver circuits are dis¬
cussed in Vol. 23, Chap. 22.

666

MOVING-TARGET INDICATION

[Sec. 16-17

by radar receivers. It will be noticed that several extra stages are neces¬
sary to obtain this type of limiting. The coherent oscillator circuit has
already been described. The function of the “coherent oscillator locking
test” channel will be discussed in Sec. 16-21.

Fig. 16-30. —Block diagram of a typical MTI receiver: i-f limiting; balanced detector;
intermediate frequency 30 Mc/sec; l-fisec pulses.

Figure 16-31 shows the circuit of the balanced detector, which con¬
verts phase changes at the input into amplitude changes at the output
with a fair degree of linearity. 1

The theory of the circuit is given in Vol. 23, Chap. 22.

Sec. 1618]

THE SUPERSONIC DELAY LINE

667

16*18. The Supersonic Delay Line. —The principal elements of a
delay line are the transmission medium and the electromechanical trans¬
ducers. Because of the bandwidth required, MTI delay lines have been

operated with amplitude-modulated carrier frequencies in the region of
15 Mc/sec. The transducers consist of piezoelectric quartz, X-cut and
optically polished. The two transmission media so far used are mercury

Fig. 16-32.—A supersonic mercury delay line of variable length.

and fused quartz. The principal factors encountered in line design have
been treated in detail elsewhere 1 and will be briefly reviewed here.

Liquid Lines .—The simplest delay line is a straight tube with parallel
transducers at the end. A laboratory design of mercury line has been
shown in Fig. 16-10. A model for field use is shown in Fig. 16-32. The

1 Chap 6, Vol. 17; Chap 24, Vol. 19, Chapa. 13, 14, Vol. 20.

668

MOVING-TARGET INDICATION

[Sec. 16-18

latter line is variable in length over a small range to compensate for tem¬
perature changes or to allow the use of MTI on more than one beam of a
synchronized multibeam system. The screw thread and sliding alignment
surfaces are external to a stainless-steel bellows whose length is three-
quarters the length of the delay line. The mean delay is 586 Msec.

The line, with expansion chamber
and electrical end housings, is
shown shock-mounted in a ther¬
mally insulated box. This line
was designed for use at 30 Mc/sec.
Quartz-to-quartz parallelism is
maintained to 0.03°

A straight tube having the
length necessary for low-PRF sys¬
tems would be inconvenient for
field use. Several methods of
folding delay lines have been suc¬
cessfully used, one of which is
shown in Fig. 16-33. In addition
to the intersecting truss members,
there can be seen six vertical tubes.
Four of these constitute the signal
delay line; the other two, the
trigger-generating line. Begin¬
ning at the end cell on the nearest
Fig. 16-33—A folded mercury delay line. top corner, the signal passes down

the nearest tube, is reflected twice, passes up the tube next left, etc., until
after six reflections it enters the cell at the extreme right. The trigger
line is half as long, giving rise to a double-frequency trigger which is
divided electrically.

This type of line is relatively easy to make. The two end surfaces of
the main assembly are ground flat and parallel after welding. The
tolerance in parallelism is eased for the critical signal line by the auto-
collimating effect of the three reflector blocks. Freedom from warping is
insured by the use of hot-rolled steel and by annealing. The corner-
reflector blocks are precision-ground pieces, but of a shape familiar to a
tool-making shop. These reflectors bolt without gaskets to the main end
plates beneath the visible housings. Thus, the only gaskets that might
affect alignment are those beneath the end cells. Air is removed from the
line; thermal expansion is accomodated by a bellows within the cylindrical
housing on the side of the line. A positive pressure is maintained so that
any leakage is outward. The line normally operates with end cells down¬
ward so that small remaining air bubbles will collect above the corner

Sec. 1618]

THE SUPERSONIC DELAY LINE

669

reflectors out of the path of the beam. The tubing has an inside diam¬
eter of | in. The total signal delay is 1000 Msec. The carrier frequency
is 15 Mc/sec, and the pulse length is £ ^sec.

Another delay-line arrangement that is feasible but has not seen field
service is the mercury tank. A quartz plate oscillating in a large volume
of mercury will generate a “free-space” beam whose width can be cal¬
culated from diffraction theory. If such a beam is incident upon a wall
of the mercury container, it can be specularly reflected without appreci¬
able loss, providing the angle of incidence is sufficiently large. Labora¬
tory delay lines have been constructed consisting of a mercury-filled tray
within which a supersonic beam is repeatedly reflected from the side
walls in any of a variety of geometrical patterns until the beam reaches the
receiving quartz. Designs that have been proposed in the past have
appeared inferior to the folded line as regards weight, size, or ease of
construction, and have consequently not been pursued to the engineering
stage.

The Fused Quartz Line .—Solid media offer difficulties not encountered
in liquids. The uncontrolled transfer of energy between compressional
and transverse modes will give rise to pulse distortion and multiple
echoes. Such difficulties may occur at the boundaries of the material or
at points of inhomogeneity. Since sound velocity in solids is greater than
that in mercury by a factor of about 4, the beam spread is greater and the
delay path longer. However, a 420-Msec line giving acceptable perform¬
ance has been made of an annealed fused quartz block 6 by 17 by 18 cm.
This line operated at 15 Me/sec with a pulse length of less than 1 Msec. An
internal reflection pattern was employed which resembled the pattern of
the liquid delay tank, but use was made of the specific elastic properties of
fused quartz to achieve a controlled transfer of energy between compres¬
sional and transverse modes. The result was that the energy in the
transverse mode could be reduced to zero after each group of three
reflections. Although much engineering remains to be done, it is possible
that delay times can be extended to 1000 or 2000 Msec by the use of
larger blocks.

End Cells .—The various ways of mounting the quartz crystals may be
classified according to whether the backing behind the crystal is intended
to absorb or to reflect. Spurious echoes may reach the receiving crystal
in either of two principal ways. If the vibratory signal enters the backing
material it may emerge later, unless care is taken to absorb or disperse the
energy. On the other hand, if the energy is predominantly reflected at the
surface of both end cells by the use of a mismatching material in contact
with the piezoelectric quartz, the signals may return to the receiving end a
second time after reflection, first from the receiving and then from the
transmitting quartz.

670

MOVING-TARGET INDICATION

[Sec. 16-18

The end cell shown in Fig. 1610 is highly efficient as an acoustic
absorber but is useless outside of the laboratory because the unsupported
quartz plate can be cracked by standing the line on end. Several methods
of supporting the crystal from the rear while retaining the mercury as a
backing medium have been tried. A more promising approach to the
design of an absorbing end cell is the use of lead soldered to the quartz.
The lead provides a good acoustic match to mercury, while strongly
attenuating the supersonic energy that it receives.

The use of absorbing end cells is
preferable with mercury lines of
delay less than about 500 y sec.
With longer lines, the use of reflect¬
ing end cells may be better for two
reasons. In the first place, attenu¬
ation always takes place within the
mercury. Thus, by the choice of
carrier frequency and tube diameter,
it is possible to reduce the amplitude
of unwanted echoes to less than 1 per
cent of the desired signals. Second, the use of absorbing end cells costs
12 db (6 db per end). The construction of a reflecting cell is shown in
Fig. 16-34. The quartz is supported directly by the steel electrode.
The occluded air film provides the necessary acoustic mismatch.

Design Constants for Mercury Lines .—The delay time is presumed to be
given. From it, the length of mercury column can be calculated accord¬
ing to the formula

Fig. 16-34.—A reflecting end cell for a
mercury line.

D = 1,(17.42 + 0.0052T),

(18)

with an estimated probable error of 0.06 per cent between 10°C and 40°C,
where D is the delay in microseconds, L the length in inches, T the centi¬
grade temperature.

The two quantities to be chosen, along with the line configuration and
the end-cell type, are the carrier frequency and tube diameter. These
enter into the design mainly in connection with attenuation, bandwidth,
and demodulation. The over-all delay-line attenuation can be divided
into two parts: that which occurs in the medium itself, and that which has
to do with the efficiency of the quartz crystals in converting electrical
energy into acoustic energy.

Both carrier frequency and tube diameter affect the attenuation that
occurs within the delay medium. The free-space frictional attenuation
in liquids is proportional to the square of the frequency. In mercury this
attenuation is about 0.11 db/in. at 10 Mc/sec. The attenuation due
to wall effects is less clearly understood but is believed to vary inversely

Sue. 16-18]

THE SUPERSONIC DELAY LINE

671

as the diameter of the tube and directly as the square root of frequency.
An experimental value is 0.1 db/in. at 10 Mc/sec with a -j-in. tube.

The efficiency of the crystals can be stated in terms of the transfer
impedance of the delay line, as follows:

V 2 _ 2R X R 2

7T " ~rT’

where 1 1 is the current driving the transmitting crystal, V 2 is the voltage
developed across the receiving crystal, R 1 is the load resistance shunting
the transmitting crystal and R 2 that for the receiving crystal, Rk is the
electrical equivalent of the characteristic impedance of the line. The
equation applies to the case of reflecting end cells. Now Ri and R 2
depend on the bandwidth that is required, since the bandwidth at each
crystal is inversely proportional to the product of the loading resistance
and the total capacity, including the electrostatic capacity of the crystal
and the stray capacity of cable connections. This assumes that single-
tuned coupling circuits are used.

The characteristic impedance R k is inversely proportional to the
active area of the crystal and to the square of the frequency. At 10
Mc/sec the value is 22,000 ohms for an active area of 1 in. 2 With this
area the total capacity at each crystal is about 50 nrf, and the bandwidth
is then 3.8 Mc/sec per end if R x — Ri = 300 ohms. These values give
a transfer impedance of 8.6 ohms. It will be noticed that no account is
taken of the inherent bandwidth of the crystals.' This is because the
bandwidth for both crystals in series is more than -py of the carrier
frequency.

It can be shown that, for a given bandwidth, the transfer impedance
is a maximum when the crystal diameter is chosen so that the active
crystal capacity equals the total stray capacity.

The carrier frequency for mercury lines may range from 5 to 30
Mc/sec, with the most usual values in the range from 10 to 20 Mc/sec.
Choice of frequency depends upon the" delay-line attenuation, and on
the fact that the number of carrier cycles per pulse must be sufficient to
allow accurate demodulation.

It was mentioned earlier that the quartz-mercury combination has
adequate inherent bandwidth. In a reflecting end cell the response is
actually flat over a frequency range equal to 40 per cent of the carrier
frequency. This allows a simple cure for a practical difficulty that is
frequently encountered with this type of cell. Because the reflecting end
cell is loaded on one side only, a slight smudge or spot of scum will unload
a portion of the crystal area without removing the electrical excitation.
When this happens, the pass band exhibits sharp spikes at the resonant
frequency of the quartz. These seriously impair the quality of cancella-

672

MOVING-TARGET INDICATION

[Sec. 16-19

tion. This difficulty can be avoided by operating at a carrier frequency
that is far off crystal resonance but still on the flat part of the loaded
characteristic.

16-19. Delay-line Signal Circuits. —The delay line is a low-impedance
device with a large attenuation; it is mechanically awkward to mount the
line physically close to vacuum-tube circuits. These facts combine to
make the delay process electrically expensive. The subject of delay-line
signal circuits has been treated at length in another book. 1 It will be
reviewed here.

Line-driving Circuits .—The requirement that the signal output shall
be well above the statistical noise level generally means that considerable
power must be furnished to the transmitting crystal.

If an i-f signal from the receiver is to drive the line, amplification is
required. Otherwise, a carrier frequency must be modulated with a
video signal. This problem is similar to that of the television transmitter.
Only a reasonable degree of linearity is required; the response slope should
not vary by more than perhaps 15 per cent. The real difficulty arises
from the proximity of the carrier and video frequencies and from the
requirement that the delayed and undelayed video signals must cancel
to 1 per cent in amplitude.

In simple modulators, modulation components are removed from
the modulated carrier channel by frequency discrimination. If the
modulation spectrum extends to more than half the carrier frequency,
spurious transients in the carrier pass band may arise in two ways.
The modulation spectrum may have components that lie in the carrier-
channel pass band, or modulation components may add to carrier side¬
band components to give components lying within the carrier-channel
pass band. Further, spurious components may arise from frequency
modulation of the carrier oscillator by the video signal. Since the
carrier phase is random from pulse to pulse, the envelope of the summa¬
tion of all such components within the carrier pass band will vary from
pulse to pulse so that cancellation will be imperfect. These difficulties
can be avoided by the balanced modulation of a carrier amplifier driven
by an isolated oscillator. A common procedure is to use parallel-grid
modulation of a push-pull amplifier stage. Alternatively, the problem
might be solved by phase-locking the carrier oscillator to the transmitted
pulse trigger, thereby insuring a constant relative phase between each
echo and the carrier. Oscillator isolation would still be necessary, since
otherwise a strong moving target might destroy the phase coherence.

The Two-channel Amplifier .—The signal level at the input terminals
of the two-channel amplifier must be great enough so that the statistical
noise generated therein is considerably smaller than the statistical noise

1 Vol. 20.

Sec. 1619]

DELAY-LINE SIGNAL CIRCUITS

673

originating in the radar receiver. The high cost of delay-line input
power makes necessary the careful conservation of output signal. Maxi¬
mum signal-to-noise ratio is obtained with a short lead from the delay line
to the first amplifier grid. If the amplifier cannot be located within a few
inches of the delay line, a preamplifier is necessary. Low-noise input
circuits can profitably be used, but critically adjusted circuits should be
avoided, if possible, because of the difficulty of maintaining balance
between the delayed and undelayed channels.

The bandwidth of the amplifier must be sufficient to avoid serious
impairment of system resolution and the loss of system signal-to-noise. 1
In addition, the bandwidth of the delayed and undelayed channels must
be sufficient to make the interchannel balance noncritical. Bandpass
unbalance will have relatively little influence upon pulse shape if the
bandwidth of each split channel is perhaps twice that of the over-all
system.

Even though the bandwidth of these channels is large, it may still
be necessary to make an approximate compensation for two types of
unbalance. The smaller gain in the undelayed channel would ordinarily
result in a greater bandwidth. This channel should therefore be nar¬
rowed to match the other by the addition of capacity to ground in the
low-level stages. The second type of unbalance arises from the frequency
dependence of attenuation in the delay-line medium. The square-law
factor generally predominates. Compensation can be obtained by insert¬
ing in the delayed channel an LC-circuit tuned to a frequency much higher
than the carrier frequency.

Amplitude cancellation to 1 per cent implies an extraordinary degree
of linearity in the two channels. The carrier level at the canceling diodes
must be well above the region of square-law diode response. The final i-f
stages must be conservatively operated. A first-order correction for
residual nonlinearity will result if the last two i-f stages of the two
channels are identical in every respect.

Gain adjustments should be made in low-level stages to avoid the
introduction of nonlinearity. A wider range of adjustment will be
required in the delayed channel because of possible variations in delay-line
attenuation. A first-order balance of transconductance changes due to
heater voltage fluctuations will result if the same number of amplifying
tubes is used in each channel. Pentodes with high mutual conductance
frequently exhibit small sudden changes in gain as a result of either heat¬
ing or vibration. The gains of the individual channels can be stabilized
through feedback of bias derived by detection of the carrier level. A

* In coherent MTI, the signal-to-noise ratio depends upon the over-all system
bandwidth and not in any special sense upon the bandwidth up to the detector.

674 MOVING-TARGET INDICATION [Sec. 1619

more elegant approach is to measure the cancellation residual of a sample
pulse and to correct the relative channel gain accordingly.

Fig. 16-35.—Signal circuits and case for the line of Fig. 16-33; two-channel amplifier
on the wide chassis at left, video-modulated oscillator and amplifier on the narrow chassis at
right.

After detection and cancellation of the echoes in the delayed and
undelayed channels, the residual video signal must be amplified, rectified,
and limited for application to an intensity-modulated indicator such as

Sec. 16-201

DELAY-LINE TRIGGER CIRCUITS

675

a PPI. The most difficult of these operations is amplification. If
statistical noise and weak moving-target signals are to be fully visible,
they must reach the final video rectifier at a level sufficient to cause linear
operation of that detector. Since the noise level at the cancellation
detector may be as much as 40 db beneath the signal peak, a gain of
several hundred may be required between cancellation and rectification.
This video amplification is difficult because of the bipolarity and wide
dynamic range of the signals. Unless special precautions are taken,
strong signals from moving targets may draw grid current and bias the
amplifier to the point where weaker moving-target signals are lost. The
bipolar nature of the signals prevents the application of the clamping
technique, which is useful in avoiding a similar trouble with unipolar
video amplifiers. Blind spots and overshoots can be adequately mini¬
mized by careful choice of time constants, grid bias, and plate load
resistors, although several additional amplifier tubes may be needed as a
result. 1

Full-wave rectification before application to a unipolar device such
as a PPI is roughly equivalent to doubling the PRiband is correspondingly
to be recommended. Either crystal or diode rectifiers may be used.
Limiting can take place both before and after rectification.

Figure 16-35 shows the two-channel amplifier on the left, with the
delay-line box in the middle, and the video-modulated oscillator and
amplifier for driving the delay line on the right.

16*20. Delay-line Trigger Circuits. —For proper cancellation the
PRF of the radar transmitter must match the supersonic delay to of a
pulse length. Free-running oscillators for generating the trigger have
been built to fire the transmitter at a suitably constant rate. Because of
the large thermal coefficient of delay in mercury, normal fluctuations in
ambient temperature necessitate manual readjustment of such oscillators
at intervals ranging from 10 min to 1 hr. Since this amount of attention
cannot be tolerated in most applications, several methods have been
devised for automatically maintaining time synchronism between the
PRF and the supersonic delay.

Time synchronism is maintained by generating trigger pulses at a
PRF determined either by the signal delay line or by an auxiliary delay
line. The methods for doing this can be divided into two classes;
regenerative and degenerative. The regenerative method has already
been described briefly in Sec. 16-3.

The Degenerative Trigger Circuit .—A highly stable oscillator generates
the transmitter trigger, and a correction is applied to the oscillator if it
fails to match the delay line. This correction is obtained as follows,
Several microseconds before the transmitted pulse, the echo input to the

1 Nonblocking amplifier design is discussed in Secs. 5-8 and 10-4 of Vol. 18.

676

MOVING-TARGET INDICATION

[Sec. 16-20

delay-line driving circuit is desensitized by a trigger from the stable
oscillator. This trigger does three other things: it generates a sample
video pulse which travels down the line; it operates a coincidence circuit
which examines the time of arrival from the comparison amplifier of the
preceding sample pulse; and finally after suitable delay it fires the
transmitter and resensitizes the echo circuits. The coincidence circuit
supplies a variable d-c bias to the oscillator which keeps the frequency of
that oscillator in step with the supersonic delay time as measured by the
sample pulses.

This arrangement has the disadvantage that it takes a number of tubes
and, like all multistage feedback circuits, is difficult to analyze in case of
trouble. It has the advantage that, with small additional elaborations,
the sample pulse residue after cancellation can be used to control the gain
of one channel of the comparison amplifier. This type of AGC corrects
for changes in both the amplifier and the delay line.

Regenerative Trigger Circuits .—Three distinct methods have been
proposed for trigger regeneration. They differ in the way in which the
fraction of a microsecond inevitably lost in the trigger amplifier is made up
in the delayed signal channel. The compensating delay must be inserted
after the point at which the trigger pulse has left that channel but before
cancellation.

The first method is to add the required delay either at carrier or
video frequency. Unfortunately, no electrical delay lines are available
which are capable of reproducing a microsecond pulse with less than 1 per
cent distortion.

The second method involves the use of an auxiliary delay-line receiv¬
ing crystal slightly closer to the transmitting crystal than is the regular
receiving crystal. The auxiliary crystal receives the trigger pulse. The
final time adjustment can be accomplished in the trigger circuit either
mechanically by an actual shift of the crystal or electrically by the use of
a short variable delay. The disadvantages of this method lie in the
excessive attenuation in the trigger channel, the increased difficulty of
delay-line construction, and the loss of design flexibility due to the
necessity of mixing the trigger and the video signals at the transmitting
end of the delay line while preventing their interaction at the receiving
end.

The third method of trigger regeneration, already described in Sec.
16-3, is the use of an extra delay line in close association with the signal
delay line as illustrated in Fig. 16-33. This line is thermally lagged by
the box of Fig. 16-35. The method allows freedom in the choice of line
constants and of electrical coupling, with some resultant circuit simplifica¬
tion as compared with the three-crystal delay line. However, the amount
of thermal correction is not as great as in the three-crystal line, The

Sec. 18-21]

SPECIAL TEST EQUIPMENT

677

extra half-length line generates triggers at double the PRF. These are
divided by a counting circuit before delivery to the radar transmitter.

16*21. Special Test Equipment. Operating Tests .—The minimum
additional equipment required to check the components peculiar to an
MTI system can be incorporated in a single A-scope chassis. This
chassis should include video amplifiers, expanded and delayed sweeps,
and a vacuum-tube voltmeter, together with switches and permanent
connections to other parts of the system. In addition, the receiver
chassis should include the locking-test channel shown in Fig. 16-30, and
the two-channel amplifier may contain a delay-line attenuator.

By means of a rectifying crystal permanently connected to the r-f
transmission line, together with an expanded and suitably phased sweep,
the transmitted pulse envelope can be inspected for hum modulation
and mode jumping. This test can be used whenever the more general
coherent oscillator locking test shows trouble.

The locking-pulse mixer current should be monitored. This can be
done by switching the meter normally used for the signal-mixer current.

As can be seen from Fig. 16-30, the locking-test channel delays a
sample of the locking pulse by means of a short auxiliary supersonic delay
line, and then mixes this sample with the received signal. If reflecting
end cells are used, multiple reflections within the delay line will give rise
to a number of equally spaced locking pulse echoes. These echoes will
beat with the reference signal. The presence of cycles within the echoes,
when viewed on an expanded A-scope, will show when the local oscillator
is out of tune. Since the coherent oscillator is unlikely to drift, the
tuning of the local oscillator to give maximum receiver response needs to
be checked only rarely.

The principal function of the locking-test channel, as its name implies,
is to reveal any unsteadiness in the original locking pulse or any failure of
the coherent oscillator to lock properly.

An attenuator and appropriate switches can be built into the input
circuits of the two-channel amplifier to permit measurement of delay-line
attenuation.

Checking and adjustment of cancellation can be done while the radar
is operating by mixing a delayed video pulse with the signals before
cancellation. The delay can be chosen to bring the test pulse to a range
position near the outer edge of the PPI, and adjustments can then be
made for the best cancellation of the video pulse.

Because of the several gain controls in series in the receiving train,
a d-c vacuum-tube voltmeter is necessary to check the carrier level at
the cancellation detectors.

Testing MTI Oscillator Stability .—It has been shown in Sec. 16-4 that
free-running frequency stability of a high order is required of the local

678

MOVING-TARGET INDICATION

[Sec. 16-21

oscillator. A similar type of stability is required of the coherent oscilla¬
tor. The apparatus designed by S. Roberts 1 for measuring oscillator
stability has two functions to perform. The first is the quantitative
determination of the rate of change of frequency. Because a precise
calculation of phase error requires the assumption that the modulating
frequencies are small, the second function is to check the accuracy of this
assumption. This is done by changing the time constant of the measur¬
ing circuit.

A block diagram of the apparatus used for testing local-oscillator
stability is given as Fig. 16-36. The difference frequency of 70 kc/sec is
obtained by mixing the power from two oscillators in a crystal rectifier.
One of these oscillators can be a reference standard against which the

Fig. 16-36.—Block diagram of oscillator stability tester.

other is compared. The output signal from the mixer is amplified and
applied to a frequency discriminator circuit. The voltage applied to the
discriminator is monitored by means of a vacuum-tube voltmeter and is
always adjusted to the same Value. The voltage output of the dis¬
criminator is linearly related to the difference frequency. This discrim¬
inator output voltage is applied to a differentiating circuit consisting of a
resistor and condenser. The average voltage across the resistor, pro¬
portional to the average rate of change of the difference frequency, is
measured by a voltmeter. Headphones assist in the identification of the
frequency of any modulation that may exist.

To measure the stability of a coherent oscillator, it is allowed to run
freely. For the crystal mixer of Fig. 16-36 is substituted a 6SA7 mixer,
whose third grid is connected to the output signal of the coherent oscilla¬
tor. Signals from a quartz-controlled standard oscillator are applied to
the first grid of the mixer. The difference frequency between the coher¬
ent oscillator and the standard is chosen as 70 kc/sec.

1 Loc. cit.

Sec. 16 21]

SPECIAL TEST EQUIPMENT

679

Subclutter Visibility Measurement .—A block diagram of a subclutter
visibility meter suitable for measuring the internal performance of most
MTI systems is shown in Fig. 16-37. An i-f pulse originating either in
the locking-pulse mixer or in a separate generator is modulated, delayed
and injected into the receiver channel. This same pulse locks the
coherent oscillator. The delayed pulse is modulated in phase and in

To receiver

Fig. 16-37.—Subclutter visibility meter.

amplitude by a controlled amount at a controlled doppler frequency, so
that it imitates a moving target in clutter. The minimum percentage
modulation for threshold signal visibility is a measure of subclutter
visibility. Although the simple modulation scheme shown does not
provide an exact duplication of a moving-target echo, it is believed to be
equivalent for test purposes. The meter does not measure the loss of
subclutter visibility due to fluctuations in the clutter produced by scan¬
ning or the wind. It measures only the quantity K 3 in Eq. (28).

CHAPTER 17

RADAR RELAY

By L. J. Haworth and G. F. Tape

INTRODUCTION

From the standpoint of the effectiveness with which a radar collects
information, the location of its antenna is of supreme importance. In
the use of the information much depends upon the location of the indi¬
cators. “Radar relay” is a means for separating these two components
so that each can occupy the most favorable site or so that indicators can
be operated at several places simultaneously. As the name implies,
the radar data are transmitted from the source at which they are collected
to some remote point by means of a radiation link.

17-1. The Uses of Radar Relay. —Control of aircraft in either military
or civilian applications requires the review and filtering of a mass of
information gathered from many sources, of which radar is only one.
Control centers are, therefore, located at sites chosen for their operational
convenience, whereas radar locations are chosen mainly for terrain and
coverage reasons. Sometimes it is desirable to collect the data at great
distances from one or more fixed land stations. Advantages are also
gained by obtaining the data at an airborne site with its extended horizon,
but displaying and using the data on the ground or on a ship. On the
other hand, occasions arise in which an aircraft can usefully employ
information collected from another site. In any of these cases, the
possibility of multiple dissemination of the data to many points offers
attractive possibilities.

Prior to the advent of radar relay such transmission was done by
voice or not at all. Since the average operator can pass on only about
five data per minute this method is far too slow for any rapidly changing
complex situation, in addition to being rather inaccurate. Any really
sophisticated use of radar data at remote points therefore demands the
use of some sort of relay technique.

Two general types of situation arise: (1) those in which the data are
transmitted between fixed points on land, in which case it is possible to
use fixed, narrow-beam antennas at both ends of the relay link (or, if the
information is to be broadcast from a single antenna, to use directive
antennas at least on the various receivers); and (2) those in which one or
both sites are moving, in which case the antennas must be either omni-

680

Sec. 17-2]

THE ELEMENTS OF RADAR RELAY

681

directional or controlled in direction. The first situation is by far the
simpler from the technical standpoint since large antenna gains can be
used in a very simple manner.

17-2. The Elements of Radar Relay. —One obvious method of relaying
radar information is to televise an indicator screen at the radar site and to
transmit the information by existing television means. This system
leads to a loss both in signal-to-noise ratio and in resolution because
persistent displays do not televise well. Furthermore, any single
televised display would have to be a PPI presenting the maximum radar

Radar station

Display station Trigger pulse

Fio. 17*1.—Elements of a simple radar relay system. In some cases electrical data from
the analyzer can be used directly to generate the indicator sweeps.

range, with the result that much inherent resolution is immediately lost
even though expanded displays might be used at the receiving end. The
first, but not the second, of these difficulties might be overcome by storing
the information on an Orthicon or other storage device rather than on a
cathode-ray tube.

A far superior method is to transmit the original radar data in such a
way that any desired displays can be produced at the receiving location in
exactly the same way as can be done at the radar itself. To do this, it is
necessary to provide at the receiving station: radar video signals, the
modulator trigger (or the pulse itself), and a mechanical motion (or its
electrical equivalent) that faithfully reproduces the motion of the scanner.

The elements of a system for transmitting this information are
indicated in Fig. 17T. The radar data are delivered from the set to a
“synchronizer” which arranges them in proper form to modulate the

682

RADAR RELAY

[Sec. 17-2

transmitter. At the receiving station, the receiver amplifies and demodu¬
lates the incoming signals and delivers the results to an “analyzer.” The
latter performs the necessary sorting into video signals, trigger pulse, and
scanner data. The video and trigger are delivered immediately to the
indicator system. The scanner data must usually be modified in form
before being passed on either to the indicators for direct use in electrical
display synthesis, or to the “scan converter.” The scan converter uses
these data to construct a duplicate of the scanner motion that can be
used to drive a position-data transmitter associated with the indicators.

Since the requirements of the actual transmission and reception are
very similar to those of television, slightly modified television transmitters
and receivers can be used. Together with the antennas, etc., they will
be referred to as the “radio-frequency” (r-f) equipment. The remaining
components will be called the “terminal” equipment.

Except, perhaps, when microwave frequencies are used in the radio
link, the ultimate limit of sensitivity is usually set by the degree of outside
interference rather than by the inherent signal-to-noise ratio of the
receiver. Many factors must be considered in trying to minimize the
effects of this interference.

1. The strength of the desired signals at the receiver input terminals
should be made as high as feasible compared with that of the
interference. This is chiefly a matter of making proper choice of
frequency, transmitter power, and antenna characteristics.

2. The data signals should, as far as possible, be made unlike the
expected interference in signal characteristics, and every advantage
should be taken of these differences in the receiving equipment.

3. In certain cases a favorable signal-to-interference ratio can be
enhanced by techniques such as the use of wide deviation ratios
with frequency modulation.

METHODS OF SCANNER-DATA TRANSMISSION

In even the simplest situation, the relay link must transmit the radar
video signals, the trigger pulse, signals descriptive of the scanning, and
sometimes range and angle markers. 1 In more complex cases some or all
of these items may be duplicated, and additional data such as beacon or
Identification of Friend or Foe, IFF, signals may be involved. One of the
major problems of radar relay is to find economical methods of carrying
all this information at one time. In the next few sections it will be
assumed that a single transmitter is to relay one set of data of each

1 Range markers need be transmitted only if some error is unavoidably present in
the timing of the modulator trigger pulse. Angle markers, on the other hand, furnish
a convenient check on the accuracy with which the scanner motion is followed.

Sec. 17 - 3 ]

SCANNER-DATA TRANSMISSION

683

variety. Complications introduced by multiple sets will be described
later.

17-3. General Methods of Scanner-data Transmission. —Simultane¬
ous transmission of video signals and range and angle markers is rela¬
tively simple. Marker signals need only be mixed with the video
signals; no separation is performed at the receiver. Trigger pulses can
also be mixed with the video since there is no conflict in time, but some
method of separating them at the receiving station must be provided.
If the pulses are transmitted at a higher power level than the video
signals, the difference in voltage amplitude can be used as a criterion.
This high-level transmission of pulses is usually done with amplitude-
modulated r-f equipment, since the brevity of the pulses allows high pulse
powers, with attendant signal-to-interference gain, to be obtained cheaply
(Secs. 17-11, 17-12), but it is not feasible with frequency-modulated
equipment. The alternative is to separate the signals in time, the video
signals being excluded from the transmitter during an interval prior to
and including the pulse. The trigger channel at the receiving station is
blocked by an electronic switch except when the pulse is expected.
Means for accomplishing both of these separation methods will be
described later.

Relaying the scanner data is much more complex. It is not feasible
to transmit the numerical value of an angle by a proportional amplitude or
frequency modulation of an r-f carrier. It is possible to devise methods
whereby certain functions (e.g., the sine and cosine) of the scan angle can
be used to modulate two or more subcarriers 1 directly by means of slowly
varying voltages; this has been done in the laboratory. It has been
found far more effective to convey the information through the medium
of periodic signals whose frequencies or repetition rates are several times
those involved in the scanning and whose characteristics are in some way
descriptive of it. Since scanning frequencies lie in the interval from
zero to a few cycles per second, the scanner data signals usually have
periodicities in the audio range.

The signals mentioned above can take either of two forms.

1. Continuous a-f signals can be used, the information being carried
in terms of the amplitude, the frequency, or the phase with respect
to a fixed reference. Up to the present time this technique has
been very little used.

2. Pulse-timing techniques can be applied. Data can be transferred
in terms of the frequency of a single train of pulses, the degree of

1 A subcarrier is a sine wave, usually in the audio- or video-frequency range, which,
after it has been modulated by the information-bearing signals, is used to modulate an
r-f, carrier.

684

RADAR RELAY

[Sec. 17-3

staggering of two trains, or the lapse of time between a “basic”
pulse which is one of a train and a second pulse occurring a con¬
trolled time later in the same cycle.

Omitting for the moment all questions of amplitude versus frequency
modulation, and all problems of external interference, the choice of a
data-transmission system involves three intricately related questions:
(1) how to avoid interference with the video and trigger signals and
mutual interference among the various data signals; (2) whether to use
c-w or pulse methods; (3) which geometrical quantities among those
descriptive of the scanner motion can best be chosen for transmission.

Since the video signals contain frequencies from nearly zero up to a
few megacycles per second it is not feasible to separate scanner data
signals and radar echo signals on a basis of their frequency components.
This leaves the two alternatives of time-sharing within the radar pulse
cycle, or the use of one or more subcarriers.

In the time-sharing method the scanner data are sent during the
“rest” interval at the end of the radar cycle when the indicators are idle
and the video signals are not useful. The interval can be occupied by as
many signals as are necessary to carry the information. Pulse-timing
techniques are usually used with time sharing since they are somewhat
simpler and probably more accurate than those involving interrupted
continuous waves. It is usually possible to allow some of the pulses to
take part in the transmission of more than one piece of data. Often the
modulator pulse itself is used as part of this timing system.

When the subcarrier method is adopted, it is customary to use con¬
tinuous waves rather than pulses, partly for reasons of simplicity and
partly because of smaller bandwidth requirements. When c-w signals are
used, the various components of the scanner data can be distinguished
from one another by sending each on a separate subcarrier, or by using a
different audio frequency for each signal and transmitting them together
on a single subcarrier.

The geometrical quantities transmitted can be chosen in various ways,
depending on the application. The most important are:

1. Changes in the orientation of the scanner can be transmitted by
means of a wave train in which one cycle represents an advance of
the scanner through a given small increment of angle. If the
scanner velocity is constant or changes only slowly, the wave train
can be a sinusoid, or convertible into a sinusoid; hence a synchro¬
nous motor may be used in the scan converter. Some method of
adjusting the initial phase of the converter relative to the scanner
and of recognizing alignment must be provided. This general

Sec. 17-4]

METHODS OF COMBATING INTERFERENCE

685

method is satisfactory only for transmitting continuous rotation at
a fairly constant rate.

2. The angle itself can be transmitted in terms of the relative phases of
two sets of periodic signals which are usually either sinusoids or
pulse trains (Sec. 17-5). Since this is a single-valued method, no
zero-phase adjustment need be made. It can therefore be used for
sector scanning, or for interrupted scanning. The data can be used
to position a scan converter by means of a phase-sensitive mecha¬
nism, or they can be used directly to provide electrical information
for such an indicator as a B-scope.

3. The values of the sine and the cosine of the scan angle can be
transmitted in any of several ways (Sec. 17-7). Transmission of
sine and cosine is also a single-valued method. The data can be
used to control a scan converter or directly in electronic PPI’s or
related indicators.

17-4. Methods of Combating Interference. —Aside from providing
the best possible signal-to-interference intensity ratio at the receiver
input, the principal method of minimizing the effects of interference is to
take advantage of differences between the desired and the undesired
signals. The differences, which should deliberately be made large, can be
exploited both by using them as a basis for excluding the undesired signals
from the operating device and by making that device as insensitive as
possible to interfering signals that are not excluded. Unwanted signals
can be rejected by frequency discrimination; the bulk of the interference
is excluded in this way. However, since it is always necessary to have a
finite bandwidth to admit the necessary information, some interference is
likely to get through to the analyzer.

In the case of the scanning data, it is often possible to protect against
transient interference (or absence of signals) by exploiting electrical or
mechanical inertia. Care must be taken that the inertia does not
appreciably inhibit satisfactory response to scanning accelerations, a
serious restriction if sector scanning is involved.

A second, and more promising, method of approach is to take advan¬
tage of approximate knowledge of what the real signals should do by
excluding completely all information that does not closely agree with
expectation, just as tuned circuits or filters reject signals outside their pass
band. The knowledge on which to base the selection may be available
a priori, or it may depend partly on a memory of what has happened in the
immediate past.

As an example of such methods consider an information-bearing pulse.
Very similar pulses with the same frequency components as the signals
are likely to be present in the interference and of course cannot be

686

RADAR RELAY

[Sec. 17-4

excluded by the receiver. If, however, these interfering pulses are not too
numerous and strong, it is possible to provide almost complete protection
against them by using a “coded” signal to represent the pulse, or by
excluding all pulses that do not come within the narrow time interval
which follows the last useful pulse by the known repetition period, or by
doing both.

The most usual type of coding consists of a group of pulses succeeding
each other by precise, unequal time intervals. The responsive circuit at
the receiver is arranged to recognize only a group with precisely these
spacings. A similar combination is extremely unlikely to occur in the
interference.

A common type of coding and a simple method of producing it are
illustrated in Fig. 17-2. When the blocking oscillator V i„ is triggered
by an incoming signal, it produces a pulse of less than 1-jusec duration.
The sharp positive pulse at B is passed through the 2-Msec delay line to the
grid of V u. The negative pulse on the plate of V lb passes back to V la and
retriggers it to produce a second pulse delayed by 2 Msec (Waveforms A
and B ). The cumulative effect of the two actions charges C i sufficiently
to cut off Vi a for a time so that further regeneration does not take place.
The first pulse is driven down the 4-Msec delay line by V Vj and triggers Via
after a total delay of 6 Msec. The firing of V charges C 2 sufficiently to
cut off the tube so that the second pulse, which arrives 2 Msec later, cannot
trigger it. Thus three pulses occurring at 0, 2, and 6 Msec appear across
resistance R and pass to the mixer to be combined with the video and
other signals.

Other combinations of time delay can, of course, be used. The
individual delays should not only be unequal, but within reason each
should be great enough to prevent radar or other interference pulses from

Sec. 17-4]

METHODS OF COMBATING INTERFERENCE

687

bracketing pulses. They are not, however, usually made greater than a
few microseconds because of the bulkiness of longer delay lines.

A method of decoding the three pulses is shown in the upper part of
Fig. 17-3. Signals from the receiver are differentiated by the grid circuit
of amplifier V ia so that blocks of signals are not passed. If the incoming
pulses are large enough, the tube can be biased past cutoff in order to
exclude signals at lower levels (as, for example, when amplitude is to be
used as a basis of discrimination between pulses and video signals).
Weak interference can also be excluded in this way. V 2 acts as a limiting

Fig. 17-3.—Interference blanker and triple-pulse decoder.

amplifier. After passing through the cathode follower I 7 3o , each pulse
arrives twice at the grid of Vit,, once with no delay and once with a
2-nsec delay. Six pulses will therefore arrive at V 3 b, and two of these, the
first delayed pulse and the second undelayed pulse, will be in coincidence,
as the waveform diagram shows. Thus five pulses, the second of which
has double amplitude, will arrive at the grid of Vi after a further delay of
4 nsec. V t is so biased that only the large pulse lifts the grid past cutoff.
Since the total delay of this pulse is 6 //sec, its arrival will coincide with
that of the third undelayed pulse on the suppressor of V t . At this time,
and this time only, the plate of V 4 receives a signal and fires Vs„. This
event cannot occur if any of the pulses is missing; therefore interference
can produce a result only when three spurious pulses occur with approxi¬
mately the correct spacing. Differentiation at the input circuit prevents

688

RADAR RELAY

[Sec. 174

long signals from straddling two or more pulse intervals and thus provid¬
ing false coincidences. It cannot, of course, prevent such blocks of
signals from saturating the receiver and excluding the desired pulses.

A brief analysis of the effectiveness of the coding is worth while.
Periodic pulses cannot give a response from Vi unless their frequency is
greater than the reciprocal of the delay times in the coding. Random
pulses or noise do, however, have a finite probability of initiating a
response. To calculate this probability suppose that there are n random
pulses per second and let r be their length. Then the fractional time
during which the grid of V#, is receiving signals through the delay line is nr.
The probability that a signal from a given undelayed pulse will overlap
that from the delayed pulses is therefore 2 nr, the factor 2 entering on the
assumption that any overlap at all will produce a result. Thus the
number of reinforced signals reaching the grid of V t each second is 2 n\.
Since the probability that one of these will coincide with a pulse on the
suppressor grid is nr, 1 the total number of pulses triggering V t each
second is 2 n 3 r 2 . This is to be compared with the number n of inter¬
fering signals originally present, the ratio of improvement being

n/2n 3 r 2 = l/2n 2 r 2 .

If, for example, r = 1 gsec and n = 10,000, this ratio is 5000. The ratio
improves for smaller n and vice versa.

If the signal being relayed is the firing time of the modulator, the
firing should, if possible, coincide with the transmission of the third pulse.
If the modulator can be triggered with sufficient accuracy, the output
connection indicated in Fig. 17-2 can be used for this purpose. If, on
the other hand, the modulator is self-synchronous, its pulse must be used
to trigger the coder. The synchronizing pulse at the receiving station,
which must await the arrival of the third pulse, will be 6 Msec late. If
this error cannot be tolerated, the video signals must be passed through a
6-Msec delay line before they reach the indicators.

Figure 17-3 also illustrates one method for excluding all signals
except during an interval surrounding the expected time of arrival of the
desired signal. The coincidence pulse from the plate of Fa is passed, after
buffering in V y,, through a 2-gsec delay line, and is used to trigger the
flip-flop circuit formed by F^ and F 6 & (Sec. 13-7), in which circuit
the latter tube is normally off. After the flip-flop has been triggered, the
current through F«, lifts the cathode of F la , cutting this tube off by an
amount greater than the signal level. The flip-flop is timed to reverse
shortly before the next desired signal is expected. Fu prevents an
appreciable pedestal from appearing on the common plate circuit
since it is turned on when F \ a is turned off and vice versa. If the signals

1 The factor 2 does not enter again.

Sec. 17-5]

THE METHOD OF INCREMENTAL ANGLE

689

are large enough to allow V 1o to rest below cutoff even when on, V ib is
unnecessary. Alternative types of video switches are described in
Sec. 13-9. The sensitive time must be long enough to allow for all
uncertainties in the periodicity of the incoming signal and for changes in
the flip-flop circuit timing.

This method can also be used to distinguish between different signals
which have been transmitted on a time-sharing basis: for example, to
separate pulses from video signals. If the coincidence circuit is to be
used to decode more than one set of pulses, the flip-flop can be triggered
by the last set or by a pulse from a delay circuit which spans the signal
interval. More often, a train of switches is necessary to separate the
various pulses from one another after decoding so that no switch is
necessary at the input circuit. Somewhat more elegant methods which
allow narrower open intervals can be used in certain special cases in which
the opening of the switch can be controlled from a sequence of events
within the cycle. Various arrangements will appear in later sections in
connection with specific methods of data transmission.

17-6. The Method of Incremental Angle. —This section and the next
three will describe various specific methods of relaying the scanner
information, the basis of classification being the geometrical quantities
used.

As stated in Sec. 17-2, the method of angular increments usually
involves, as a final stage, a synchronous motor driven by a sinusoid.
Three methods of relaying the necessary data have been used.

In the first method, the sinusoid itself may be transmitted directly
on a subcarrier. The extra expenditure of power involved is usually not
justifiable for this rather inflexible method, especially since the pulse
methods are extremely simple.

As a second method, the modulator pulses themselves can be used to
represent the increments of scanner angle 1 if the scanner motion can be
made sufficiently constant to control the modulator triggering satis¬
factorily. Such a system is represented in Fig. 17-4. 2 Some form of
signal generator—usually electromagnetic—geared to the scanner pro¬
duces periodic signals of frequency proportional to the scanner velocity
and suitable for the pulse recurrence frequency. These signals control a
blocking oscillator or some other device to produce sharp pulses which are
then coded for transmission over the relay link. The third pulse of the
code (from point E of Fig. 17-2) is used for the modulator trigger.

Some method must be provided for separating pulses from video

1 This is, of course, an example of time sharing in which two of the signals coincide.

1 In all the diagrams of this chapter the individual blocks are functional and are
intended to include proper input and output circuits including amplifiers, cathode
followers, blocking oscillators, etc.

690

RADAR RELAY

[Sec. 17-5

To modulator

Wave form at A

f=m

Wave form at B and I
Wave form at J
120 cps

Wave form at K

Slow time scale

AA/WWWVWWWY

I I I I I I I I I I ! I I I I I I I I I I

J_I_I_I_L_

Wave form at L
f **60 cps

Wave form at

C and H
D and I
E and M
F and G

Expanded time scale

_IU_

1 1

IN_ _

Video

Fig. 17-4.—Simple incremental-angle synchronization.

Sec. 17-5]

THE METHOD OF INCREMENTAL ANGLE

691

signals at the receiving station since otherwise video signals might occa¬
sionally produce a spurious trigger. If the transmitter provides higher
power in the pulses than in the video signals, amplitude selection can be
used, and the coded pulses can simply be passed to the transmitter.
Otherwise, the coded pulses must be distinguished in time, and the extra
equipment indicated by the dotted boxes must be used. The video
switch (Sec. 13-9) is arranged to pass video signals only when the flip-flop
(Sec. 13-7) is on, and pulses only when it is off. The flip-flop is fired by the
modulator trigger, so that video signals are passed until shortly before the
next cycle, at which time the flip-flop opens the switch for pulses until
the modulator pulse occurs again.

At the receiving station, signals from the receiver pass to a switch
which is open when a pulse code is expected. Following this switch is a
decoder similar to that of Fig. 17-3. The resulting single pulses serve to
trigger the indicators, to control the signal-selecting switch, and to provide
the rotation. The switching action is similar to that of V ia , Fu, F&., and
Fa, of Fig. 17-3, the length of the flip-flop being slightly less than that
of the flip-flop at the transmitter so that video signals are always excluded
from the decoder.

To produce the mechanical rotation, the decoded pulses first actuate
a scaling circuit, such as that of Fig. 13-20, which reduces their frequency
to twice that appropriate to a synchronous motor. The resulting pulses,
by triggering a scale-of-two circuit similar to that of Fig. 13-166, produce a
symmetrical square wave. A broadband a-f filter removes the higher
harmonics, leaving a sine wave at the fundamental frequency which, after
amplification, powers a synchronous motor that drives a data transmitter.
Proper initial phasing of the data-transmitter shaft can be made by
methods analogous to those of display-sector selection (Chap. 13);
alternatively, a controlled phase shifter can be inserted between the a-f
filter and the amplifier. A convenient index for use in this alignment can
be provided by transmitting one or more angle markers along with the
video signals, as illustrated in Fig. 17-4.

This method is restricted in its use. The requirement of a continuous
scan at a nearly constant speed mentioned in Sec. 17-3 is made even
more rigorous by the synchronization with the modulator, w-hich must
usually operate at a definite PRF. Any requirement for variation in the
scanning rate or the PRF introduces serious complexities because of the
fixed relation between these two quantities. Another drawback is that
rephasing must be done whenever the signals are interrupted or seriously
interfered with.

More flexibility is provided by a third means for relaying incremental
angle data. If the scanner and the modulator cannot be synchronized but
the scanning is nevertheless reasonably uniform, the periodic signal can be

Sec. 17-51

THE METHOD OF INCREMENTAL ANGLE

698

Point* Fig.(17.3)

y i i i m i i i i 1 1 i y —n_n_

a d _T1_Tl_

B&cAj\y\Ju\j\D\AjVAAA. e _Tl_Tl_

d I l I I I I l l l l l I *_n_E!3_JUL_riJii!Ili_

Fia. 17-56.—Jittered-pulse system, receiving station.

expressed by a sinusoidal variation in the relative timing of a pair of
pulses appearing in each pulse cycle. A method for accomplishing this is
illustrated in Fig. 17-5. The basic pulse is initiated by an external trigger
and coded by the circuit of Fig. 17-2. The third pulse, originating in V
of that figure (repeated in Fig. 17-5o), initiates the action of a time-delay
circuit consisting of a sawtooth generator Vit, a biased diode F*,, an
amplifier V and a blocking oscillator V». The need for a square-wave

694

RADAR RELAY

[Sec. 17-5

generator to switch V 2 b is avoided by the action of the positive pulse from
V 2a . During the pulse the grid current of V 2 b charges C 1 sufficiently to
block off the tube long enough to allow generation of the desired sawtooth.
The a-c voltage from a generator on the scanner acts through the cathode
follower Vib to vary the bias of the diode sinusoidally and therefore vary
the delay by steps which approximate a sinusoidal variation of about one
microsecond amplitude. The mean value is set at 5 to 10 gsec. The
delayed pulse is mixed with the coding for the basic pulse on the common
cathode resistor R and sent to the master mixer. It is not necessary to
code the azimuth pulse since its function is merely to transmit the
sinusoidal frequency; any interference strong enough to mask this pulse
would render the whole system useless in any case.

At the receiving station the basic pulse is decoded by the coincidence
circuit of Fig. 17-3. 1 The resulting pulse, taken from point Y of that
diagram, blocks the grid of F 5 & and initiates the action of the delay
circuit comprising the sawtooth generator V bb , the cathode follower F 6a ,
and the blocking oscillator V la . The tube V 2a is delayed in firing by its
excessive bias. When V 7o fires, its cathode drives the 1-gsec delay line,
and the delayed pulse returns through V n to turn off the blocking
oscillator. Thus successive 1-psec pulses, adjacent in time, appear at the
grids of Vtib and F 8 „ respectively. Their boundary time is made coinci¬
dent with the mean time of arrival of the azimuth pulse by adjustment
of the slope of the sawtooth in the delay circuit. The amplified pulse
train from point X (plate of F^) of Fig. 17-3 is applied to the cathodes of
Vti a and Fs*. Because of the bias the tubes can conduct only during the
coincidence of the azimuth pulse with the pulses on the grids. Condenser
C 2 is charged negatively by the signal from F 8 & acting through diode V%,
and positively by the signal from V so which forces negative charge to
ground through V 2a . If the coincidence time is equal on V Sa and V%,
the net result is zero. However, as the azimuth pulse moves back and
forth in time with respect to the switching pulses, the coincidence times
vary in an out-of-phase manner so that the potential of C 2 has a stepwise
variation with a sinusoidal envelope (Waveform I). This alternating
signal is passed through cathode follower F«, and a bandpass filter in
order to produce the desired sinusoid for driving the synchronous motor.

In order to minimize the number of transmitted pulses, the basic pulse
can be related to the modulator pulse in any of several ways. If the first
few microseconds of the radar cycle are not too important and the
modulator is not self-synchronous, its trigger can be the third pulse of the
coded group. No range error will result, but the azimuth pulse will
appear on the indicators at the receiving station at a range corresponding

1 The pulses can be separated from the video signals by amplitude selection, or by
time separation as in Fig. 17-4.

Sec. 17-6]

THE PHASE-SHIFT METHOD

695

to its delay time. If the modulator is self-synchronous, its firing time
must coincide with the first coded pulse. A range error in the indicators
results unless a compensating delay line is used in the video channel at one
station or the other.

If the appearance of the azimuth pulse at short range on the indicators
is not tolerable, a triggered modulator can be fired after the azimuth
pulse, the delay from the third coded pulse being precisely fixed. At the
receiver a similar delay initiated by the decoded basic pulse can be
inserted ahead of the indicators. Correct adjustment of this delay can
easily be made by observing the transmitter pulse appearing with the
video signals.

No analogous method of azimuth-pulse removal exists for a self-
synchronous modulator. It is usually satisfactory to remove the pulse by
anticoincidence methods, even though a “hole” is left in the video signal
train. Otherwise, it will be necessary to introduce between the modulator
pulse and the basic pulse a delay which is longer than the useful video-
signal interval and to transmit both pulses. 1

17-6. The Phase-shift Method.—If a sine wave is passed through a
linear full-wave phase-shifting device connected directly to the scanner,
the resulting phase shift is numerically equal to the scan angle measured
from the position of zero phase shift. By transmitting the phase-shifted
wave together with a reference signal of commensurate frequency and
fixed phase, it is possible to use the relative phases as data from which
to reconstruct the scanner angle.

C-w Methods .—A method of accomplishing this by use of c-w signals
is illustrated in Fig. 17 6. Separate subcarriers fi and f 2 are respectively
modulated by the phase-shifted sinusoid and by the reference signal,
which is the same sinusoid without phase shift. At the receiving end the
video signals and each of the subcarriers are separated by appropriate
filters and the phase-shifted and the reference sinusoids are obtained by
suitable demodulators. The reference wave is then passed through a
phase shifter similar to that on the scanner. This phase shifter is driven
by a servomechanism whose error signal is the output of a circuit which
compares the phase of the shifted wave and that of the reference wave.
A data transmitter geared to the phase shifter provides proper informa¬
tion to the indicators.

The above method is very expensive because of the two subcarriers.
Fig. 17-7 illustrates an alternative c-w method which avoids this difficulty.
Here the phase-shifted signal is a harmonic of the reference signal and is
derived from it by a frequency multiplier. Thus the two signals can be
transmitted without confusion on the same subcarrier. At the receiving

1 It is not satisfactory to use such a long delay between the basic pulse and the
azimuth pulse since small percentages of "jitter” or drift become too important.

696

RADAR RELAY

[Sec. 17-6

station the two are separated by appropriate a-f filters, and the reference
signal is passed through a frequency multiplier. The resulting sinusoid
is then passed through a phase shifter controlled by a phase-sensitive
servomechanism as before. Although this method is simple, it places

(o)

Fig. 17-6.—Phase-shift data transmission using two c-w subcarriers.

severe requirements on the audio filters. Because of their harmonic
relationship, the sinusoids must be kept extremely pure, and furthermore
any relative phase shifts introduced by the filters (or other circuit com¬
ponents) must be extremely constant with time. This is very difficult to
assure in a-f filters if they are subjected to changing temperatures.

Sec. 17-6] THE PHASE-SHIFT METHOD 697

In the above systems any one of the data-bearing signals can be
conveniently used for automatic gain control purposes.

Pulse Methods .—The pulse methods analogous to those just discussed
would consist of the use of two continuous trains of pulses derived from
sinusoids of equal or commensurate frequencies, one being shifted in
phase with respect to the other. This would require the use of at least one
subcarrier with wide sidebands, and therefore would be expensive in the

(o)

From receiver

ib)

Fig. 17-7.—Phase-shift data transmission using one c-w subcarrier.

transmitter and receiver design. An alternative would be to transmit the
pulses on the video carrier during those intervals when the echo signals are
not useful. Since the difficulty remains that the two sets of pulses must
“ride through” each other, some method would have to be found for
distinguishing the two trains. This difficulty can be avoided by transmit¬
ting one master pulse and one train of “phase-shifted” pulses on each
radar cycle and, at the receiving station, constructing the reference train
by shock-exciting an oscillator with the master pulse.

698

RADAR RELAY

[Sec. 17-6

Video signals

Basic trigger To modulator

Waveforms
Basic trigger

B Interrupted sinusoid

C Phase-shifted sinusoid

D Phase-shifted pulses
E Delayed trigger
F Switching voltage
G Selected pulse train
H Modulator trigger
I Coded pulses

i/vwwwv

AAA/VWW
..

Basic trigger
(contracted time scale)

J Video switch waveform

K Output signals _ l l ll |: llll[< — IHlllllllLt— lllllll

Pulses Video signal

Fig. 17-8o —Phase-shifted pulses transmitting station.

Sec. 17-6]

THE PHASE-SHIFT METHOD

Video

Trigger

699

Waveforms 1 _ 1111 _1_ 1 _L

Basic pulse -«- Pulse train —•- Mod. pulse

A’,B', C',D',E’,G' Same as A,B, C, etc. except later
in time by width of code

M’ ._I-L

Trigger___1—

Fig. 17-86.—Phase-shifted pulses, receiving station.

The method is illustrated in Fig. 17-8. At the transmitter the master
pulse triggers a square-wave generator (flip-flop a) which switches a
shock-excited oscillator (Fig. 13-41). The oscillation B is passed through
a phase shifter geared to the scanner, and the resulting wave C produces a
pulse train D.

In order to avoid early transients which might lead to confusion with
the master pulse (especially after coding) the first two or three pulses in
the train are excluded by switch a. This switch is controlled by a square
wave from flip-flop b; it is arranged to turn on late enough to exclude the
required number of pulses and to remain on until after the end of the pulse

700

RADAR RELAY

[Sec. 17-6

train. The remainder of the circuit is concerned with coding and mixing
the various signals and providing synchronization with the modulator
(which has been assumed to be triggerable). The basic pulse and the
pulse train are passed through the coder, as is a pulse formed at the end
of flip-flop b. This last pulse, delayed by a time equal to that of the cod¬
ing, serves as the modulator trigger. In order to separate the pulse
signals from the video signals at the receiver, if amplitude selection cannot
be used, the two are passed alternately through video switch b, which is
controlled by flip-flop c. In its normal position, the latter causes the
switch to pass signals from the coders. When the flip-flop is triggered by
the pulse to'.the modulator, the switch is reversed and video signals are
passed until the flip-flop spontaneously returns to its initial condition,
shortly before the next basic pulse, and opens the channel to pulses again.
If the transmitter is such that the pulses can be transmitted at several
times the level of the video signals, this switching need not be done since
amplitude discrimination can then be used at the receiver.

At the receiving station, the various signals must be separated and
the data abstracted and put into usable form. The signals from the
receiver are received by a switching and decoding circuit similar to that
of Fig. 17 3 except for the source of the input signal to Fm, whose function
will be explained later. For the moment assume that the switch is open.
When the basic pulse is decoded it starts a chain of events through flip-flop
a, the switched oscillator, the phase shifter, and the pulse former on the
one hand; and another chain through the delay circuit and flip-flop b' on
the other. Both culminate in switch a' and produce at its output termi¬
nal G 1 a train of pulses like that at point G at the transmitter. Mean¬
while, the transmitted pulse train is decoded and passed through switch
c, whose purpose is to exclude the basic pulse and the modulator pulse.
The two pulse trains are brought together in a “comparison” circuit
which produces a polarized error voltage if they do not coincide. (If the
two pulse trains have slightly different frequencies, because of slight
differences in the oscillators, the error voltage will refer to their “centers
of gravity.”) The amplified error voltage controls a motor which turns
the phase shifter in such a way that the error voltage is kept very small, 1
and the phase shifter and the data transmitter rotate in synchronism
with the radar scanner. The modulator pulse is selected by switch d
which is activated by flip-flop d. The latter is triggered at the moment
of recovery of flip-flop V and endures until after the arrival time of the
modulator pulse. In addition to its function at the indicators this pulse
also triggers the flip-flop (Tea, and Fa>, Fig. 17-2) controlling the switch
(Fio and Fi&, Fig. 17-2) ahead of the decoder. When this switch is

1 See Vol. 20 of this series for details of the comparison circuit and motor drive.

Sec. 17-7] GENERAL METHODS OF RELAYING SINE AND COSINE 701

closed all signals (video and interference) are excluded until the flip-flop
returns to its stable condition shortly before the next basic pulse.

17-7. General Methods of Relaying Sine and Cosine. —A complete
description of an angle can be given by expressing its sine and its cosine
in the same units. Probably the greatest variety of actual and proposed
systems for data transmission have involved the relaying of these quanti¬
ties in one way or another.

If sine and cosine of the scan angle are transmitted, these data can be
used for PPI synthesis either with or without mechanical motion. Since

A c line voltage

A sin 2n f 0 t

*T>

A cos 0 sin 2n f 0 t

_ A sin 6 sin 2rr f 0 t

Oscillators

mixer

and

transmitter

proper

Video signals
and trigger pulse

Fio. 17-9.—Hypothetical method of transmitting synchro data by c-w.

the method of synthesis has an important bearing on the choice of a relay
method, a brief discussion of the use of the data will be given. Two
general methods are possible: mechanical duplication of the scanner
motion at the receiving station (as in the previous cases), or use of the
sine and cosine voltages to produce the tw r o necessary PPI range-sweep
“components.”

Derivation of mechanical motion from sine and cosine information
requires the use of a servomechanism. Practically speaking, it is neces¬
sary, in order to reproduce the mechanical motion, to provide a-c voltages
proportional to sine and cosine, as well as a voltage of constant amplitude
for reference purposes. All voltages must have the same frequency and
phase. From the terminal-equipment standpoint these voltages could

702

RADAR RELAY

[Sec. 17-7

be obtained most simply by exciting a synchro on the radar scanner and
relaying each of the resulting voltage “components” together with
a constant reference voltage (Fig. 17-9). This method, which would
require the use of multiple subcarriers, and would thus involve excessive
bandwidth, complex multiple modulation and filtering, or both, has never
been used. Two component voltages and one reference voltage can be
provided at different a-c frequencies, but this arrangement is not suitable
for use with a servomechanism. It can, however, be used to produce
slowly varying sine and cosine voltages. These can then be used to modu¬
late alternating current of proper frequency to provide the required volt¬
age components for a synchro-controlled servomechanism. The method

Cos e

Fig. 17*10.—Use of slowly varying sine and cosine voltages: (a) production of mechanical
motion; (6) fixed-coil PPI synthesis.

is illustrated in Fig. 17-10o. It has been successfully used in connection
with various types of data transmission resulting in slowly varying sine
and cosine voltages.

In contrast to the reproduction of mechanical motion, the fixed-coil
PPI can best use slowly varying polarized direct current. 1 Since alter¬
nating current can easily be rectified to give such voltages, any of the
methods is applicable to this case. As shown in Fig. 17'106, the sweep
components are produced by sawtooth generators using the signal volt¬
ages as their source potentials so that the “sawteeth” are modulated in
the proper manner as the scanner rotates (Sec. 13T6). Through the
provision of low-impedance or multiple-output circuits for the sine and
cosine voltages, as many indicators as desired can be used. The sweep
length for each can be chosen independently of those of the others.

1 It is possible, of course, to relay the sweep components themselves. However, a
separate subcarrier would be required for each. Furthermore, each “sawtooth"
must endure for the time of the longest desired sweep, and fast sweeps must be
achieved by amplification of a short segment. Errors would be greatly magnified in
such a process.

Sec. 17*7] GENERAL METHODS OF RELAYING SINE AND COSINE 703

Signal at a Potential at b

Fig. 17-11.—Method of relaying sine and cosine by c-w on one r-f carrier.

At least two methods of supplying slowly varying sine and cosine
voltages have been successfully applied. One is a c-w method; the other
involves pulse timing.

A C-w Method .—In order to allow transmission of all the scanner data
on one r-f subcarrier, each item of information can use a different audio
frequency, the subsequent sorting being done by a-f filters. Figure 17-11

704 RADAR RELAY [Sec. 17-7

illustrates such a method. The stators of the scanner synchro are excited
by equal-amplitude signals of frequencies /i and / 2 , as are the two equal
primaries of a transformer whose secondary is in series with the synchro
rotor. The voltage across the combination is then

fi(A + B sin 6) + f 2 (A -f B cos 0),

where /i and f 2 represent the audio-frequency input voltages and A and B
are constants. Since A is greater than B, the amplitude terms are always
positive. This voltage is mixed with a constant-amplitude a-f signal of
frequency f 3 (which is used for AGC at the receiver), and the combination
is used to modulate a subcarrier of somewhat higher frequency than the
maximum required for video signals. The modulated carrier, the video
signals, and the trigger pulse are then mixed and passed on to the trans¬
mitter proper. At the receiving station, the various component signals are
separated by appropriate filters, as indicated in Fig. 17-11, and the sine
and cosine signals passed through detectors. The resulting voltages con¬
tain a d-c component of magnitude C (with respect to the detector bias
point) and a varying component of amplitude D, the sum being always
positive. The d-c component can be prevented from affecting the final
device by relating its bias level properly to that of the detector. The
scheme of adding a constant a-f component to the signal is intended to
preserve the phase sense of the components varying sinusoidally with the
scanner rotation; in this case it is considerably simpler than transmitting
a reference signal to be used in keying a phase-sensitive rectifier.

Pulse-timing Methods .—The simplest method of using pulse-timing
techniques to relay sine and cosine information can be understood by
referring to the timing diagram of Fig. 17-12. A basic pulse occurs once
each radar cycle. The delay of a second pulse is varied with respect to it
in accordance with the expression A + B sin 0, where A must be greater
than B in order that the delay shall never become negative. A third
pulse is delayed with respect to the “sine” pulse by an amount propor¬
tional to A + B cos 9. In the interpretation of the data it is only neces¬
sary to provide for each function a circuit that will develop a voltage
proportional to the time lapse between the members of a particular pulse
pair.

The essentials of such an equipment are illustrated in Fig. 17-12.
Slowly varying sine and cosine potentials are furnished by a data trans¬
mitter (which can be either a d-c excited sine-cosine potentiometer or a
two-phase synchro whose output signals are rectified in a phase-sensitive
manner). Each of these potentials controls the operation of a linear
delay circuit . The sine delay circuit is triggered by the basic pulse, and
the cosine circuit is triggered by the sine pulse produced by the sine delay
circuit. Each, gives a finite delay A when the controlling voltage is zero

Sec. 17-8] PULSE METHOD FOR RELAYING SINE AND COSINE 705

The resulting pulses are mixed with the modulator pulse and coded before
being combined with the video signals preparatory to transmission.

At the receiving station, the pulses are decoded and sorted. Each
of the pulse pairs (basic-plus-sine and sine-plus-cosine) is fed to an auto¬
matic range-tracking circuit which develops the required voltage as
indicated in Fig. 17-12. The d-c components can be removed in the way
explained in connection with Fig. 17-11.

To coding and
mixing circuits

Transmitting station

Receiving station

Cyclical

tim i ng I I I I / I f! *« a ^aA/I'aA am. A A/Ia™ AAa Aa.- .vJLv\a_ I I II, VJ iWV^a/VLwVv-

diagram Video signals b s cm Video signals

Expanded {— A+ii sin 6 — A+B cos Q

time scale I I I_ J_aJ\aAA_aaaAaaa/

Basic Sin Cos Modulator Video signals

pulse pulse pulse pulse

Fig. 17-12.—Essentials for relaying sine and cosine by pulse-timing methods.

Since this general type of synchronization equipment has seen far
more service than any other to date, it will be worth while to consider
it in more detail. The following section gives an extended treatment of
one particular example.

17-8. Pulse Method for Relaying Sine and Cosine. —Electronic
means for determining the interval between pairs of pulses will be con¬
sidered first. In Fig. 17-13 it is assumed that the basic pulse and the sine
pulse have been decoded and separated so that each is available on a

Basic pulse 1
Sine pulse _L

Point R

Point 5

Point V
Point V

Point A
Point B

r~\

706 RADAR RELAY [Sec. 17-8

Sec. 17-8] PULSE METHOD FOR RELAYING SINE AND COSINE 707

separate channel. There must now be developed a d-c voltage whose
value is at every instant proportional to the delay of the sine pulse with
respect to the basic pulse. Two of the many possible methods of accom¬
plishing this are illustrated. The components of Fig. 17-13a drawn in solid
lines illustrate a very simple method. The basic pulse triggers a flip-flop
having a lifetime slightly greater than the maximum delay of the sine
pulse; the resulting square wave is used to switch a sawtooth generator of
very low output impedance. Thus, within the life of the sawtooth, the
instantaneous voltage at S is proportional to time elapsed since the
occurrence of the basic pulse. When the sine pulse occurs, it momentar¬
ily closes the “double clamp” (similar to Fig. 13-26), thus connecting
point T tightly to point S so that the condenser is charged to the instan¬
taneous potential of S. The leakage path from T to ground is made to
have a high resistance so that the potential at T remains essentially con¬
stant until the new cycle, at which time it will take a new value corre¬
sponding to the new value of the time delay of the sine pulse. Thus the
potential at T will go through the same variations as the time delay and
will in the present case have the form A + B sin 9 as desired. This very
simple method is satisfactory provided little or no interference is encoun¬
tered. An interfering pulse will, however, cause T to take a potential
corresponding to its time of appearance. This effect can be reduced by
filtering so that no single pulse can cause any very great change, but this
filtering may cause troublesome phase lags in the desired output. A
better method of protection is to employ the output voltage to control the
opening of a switch (dotted circuits in Fig. 1713a), through which the sine
pulse must pass, in such a way that a pulse can be admitted only during a
very narrow time interval including the time when the true pulse is
expected. (Since this device as described will work only when the track¬
ing is already nearly right, some means must be provided for holding the
switch open until correct conditions are once established.) With the
addition of this protective switch, the method of Fig. 17-13a is satis¬
factory. The addition makes it, however, nearly as complex as more
elegant methods of regenerative tracking. Regenerative tracking,
although more complex, provides certain very definite advantages in
compensating for errors occurring later in the circuit.

The elements of a regenerative tracking circuit are shown in Fig.
17-136. The basic pulse triggers a delay circuit which is controlled by the
final output voltage in such a way that, assuming this voltage is right, the
delay circuit produces a pulse shortly before the arrival of the sine pulse.
The delay-circuit pulse triggers a flopover (Sec. 13-7) which in turn
sends a pulse down an improperly terminated delay line. The reflected
pulse, of opposite polarity, turns off the flopover. The resulting square

RADAR RELAY

708

[Sec. 17-8

wave from the flopover is used to open the sine pulse switch for 25 nsec
or so at the expected time of arrival of the sine pulse. 1

The delayed pulse reaches the far end of the delay line exactly at the
middle of the switching wave. The remainder of the circuit is designed
to force this “comparison” pulse into time coincidence with the sine
pulse by properly controlling the delay through adjustment of the out¬
put voltage. Various methods can be used to accomplish this adjust¬
ment. The operation of the method illustrated is described below. The
comparison pulse triggers a flip-flop. The square waves from the two
plates, one positive and one negative, are fed to the control grids of a pair
of pentodes (Fig. 17-13c), turning one on and the other off. The screen
grids, normally at cathode potential, receive the positive sine pulse. If
the pulse arrives when the control.grid of a given tube is on, that tube will
produce a negative pulse on its plate. The signals are integrated in
opposite polarity on condenser C i by means of the diodes. A negative
signal from V 3 drives a negative charge through V 3a to C 1 . A signal from
I'i drives a negative charge to ground through Fa*. The potential on C 1
is the output signal. It is returned (perhaps after amplification) to the
comparison-pulse delay circuit which it controls. Thus, if the switch¬
ing occurs before the arrival of the sine pulse, Vi conducts, C\ becomes
more positive, and the delay is increased. If the switching is too late, V 2
conducts and the delay is decreased. The process continues on successive
cycles until the delay is such that the sine pulse “straddles” the instant of
switching. The delay circuit will then follow' the variations in the delay
of the sine pulse so that the output voltage varies in the desired manner.

Figure 1714 illustrates a system in which, although it is assumed that
the modulator can be triggered, means are provided to distinguish
between the cosine pulse and the modulator pulse for other reasons.

The delay circuits in the synchronizer may be any of the varieties
described in Secs. 13-7 and 13-12, the most precise and trouble-free
results being obtained by the use of circuits similar to but not so refined
as the circuit shown in Fig. 13-36. If this type is used, the sine or cosine
voltage is used to bias the cathode of the diode, and the bias of the anode
is adjusted to give the desired delay A at zero scanner angle. The value
of B is determined jointly by the slope of the sawtooth and the amplitude
of the sine and cosine voltages from the scanner.

The basic pulse, sine pulse, and cosine pulse are passed to the usual
three-pulse coder along with the modulator trigger signal, which is derived
from a fixed-delay circuit triggered by the cosine pulse. In order that the
trigger signal shall be properly timed when decoded at the receiver, the

1 Since this interval is too narrow to allow rapid “looking in” initially or after
tracking has been lost, the circuits are arranged in a manner not shown so that in the
absence of pulses the grid remains on.

710

RADAR RELAY

[Sec. 17-8

actual modulator trigger is delayed from the signal to the coder by a time
equal to that occupied by the code. By closing the relay onto point Y
and inserting a proper electronic switch between X and Y, the modulator
trigger signal can be used as a switching signal when cyclical time sharing
with beacon or other signals is desired. If no such need is involved, the
cosine pulse can serve also as the modulator trigger signal so that delay
circuit a can be omitted and points B and C made the same.

The coded pulses and the video signals are made to share the radar
cycle by a switch operated by a flip-flop keyed by the modulator trigger,
as described in previous cases.

At the receiving station, the pulses must first be separated from the
video signals and from one another. The “sequencing” circuits which
accomplish the latter are shown on the top row of the diagram. After
being decoded, the signals pass to several swatches of the multiple-grid
variety shown in Fig. 13-27. The numbers alongside each indicate to
which grid the various signals are applied. 1 The main switch is opened
shortly before a basic pulse is expected, in a manner that will be described
presently. On passing through this switch, the pulse triggers a flip-flop
which remains on for an interval slightly greater than the largest delay
time of the sine pulse. This elevates the No. 2 grid of the sine-pulse
switch so that the sine pulse can pass through provided the No. 3 grid is
on, as explained in connection with Fig. 17-13. Once the system is
“locked in,” the narrower switch pulse on the latter grid is the deciding
factor in rejecting unwanted signals; the longer interval is useful during
the locking-in process when the shorter one cannot be used. The sine
pulse, in addition to its tracking role, triggers a flip-flop controlling the
cosine-pulse switch, and the cosine pulse similarly triggers a flip-flop con¬
trolling the modulator pulse sw itch. The modulator pulse is passed on to
the indicators and, in addition, triggers a flip-flop which closes the switch
ahead of the decoder while video signals are being received, and opens it
shortly before the next basic pulse.

A few w r ords should be said about the process of “locking in” initially
or after tracking has been lost through failure of signals or severe inter¬
ference. Since the main switch is controlled by a flip-flop, it will sooner
or later be open. If no pulse occurs during the open interval, this switch
will close, but it will be opened again by the next pulse. Sooner or later
it will receive a pulse when open. If this is the sine pulse, the sequence is
established. If it is not, the cosine-pulse switch will pass no signal, and
the process must start over. In practice, the right combination is
promptly found, and the various pulses then pass through the sequencing
circuits in the proper manner.

1 The pulses may be separated from the video signals by amplitude selection, or
by time separation as in Fig. 17-4.

Sec. 17-9] COMPARISON OF SYNCHRONIZATION METHODS

711

The tracking circuits are similar to the circuit shown in Fig. 17-13c
except for changes made to provide for a scan converter and for the fact
that the switching voltages for the sawtooth delay circuits are provided
by the same flip-flops that control the sine- and cosine-pulse switches.
A-c signals for the scan converter are obtained by modulating the 60-cps
line voltage with the sine and cosine voltages, as in Fig. 17-10a. The
regenerative tracking assists greatly in overcoming errors in the modu¬
lators by rectifying the modulated alternating current with a phase-
sensitive detector and using this result to control the tracking delay
circuit. Thus the amplitude of the modulated alternating current (which
is the quantity of primary interest) is forced to vary in the same manner
as the delay in the signal pulse, regardless of errors in the comparison
circuits, the modulator, any amplifiers, etc.

Equipment essentially like that just described has had a great deal
of use and in its final form has proved satisfactory. An entire system
using this method is described in Sec. 17-16.

17-9. Comparison of Synchronization Methods.—Not all the syn¬
chronization methods described in the previous sections have been used
on actual radar relay systems although nearly all of them have been set up
and tested in the laboratory. Because of the inadequacy of testing in
many of the cases, evaluations are difficult, but the following general
statements can be made.

Pulse vs. C-w Methods .—Pulse methods have been much more highly
developed than those using c-w transmission, partly because of the pulse-
circuit experience available at the Radiation Laboratory, and partly
because the r-f equipment available during most of the work was of the
amplitude-modulation rather than the frequency-modulation type.
However, much can be said in favor of the pulse methods from a funda¬
mental standpoint, regardless of the type of carrier modulation.

1. Since one pulse, the trigger, is involved in any method, adequate
protection against pulse interference must be provided in any case.

2. When time sharing is used within the radar cycle, the pulse methods
require less complex r-f equipment than do the c-w methods with
their requirement for at least one subcarrier. Were time sharing
with the video signals abandoned and the pulses sent on a sub-
carrier, the additional complications would be compensated by
considerable simplification and increased effectiveness of the termi¬
nal equipment. The synchronization signals would automatically
be separated from the video signals. The use of 100 per cent of
the time and the freedom from restrictions imposed by the radar
PRF would lessen the sensitivity to interference and permit much
more flexibility than is available with the time-sharing technique.

712 RADAR RELAY [Sec. 17-9

Such a method would be extremely advantageous if multiple sets
of angular data were to be relayed.

3. Pulse methods are inherently more accurate than c-w methods
since they involve either “counting” or the measurement of time—
probably the most accurate types of physical measurements that
can be made. Furthermore, no dependence whatever is placed on
the linearity of r-f modulators, amplifiers, detectors, etc., in con¬
trast to the c-w methods where all such devices must be extremely
linear and free from distortion.

On the other hand, c-w methods involve somewhat simpler terminal
equipment than do the pulse methods. They are also much less suscepti¬
ble to pulse interference, which is the type most likely to be met with at
most of the radio frequencies involved.

Comparison of Specific Methods .—The specific synchronization
methods that have been most thoroughly tested are—

1. The conveying of sine and cosine by pulses.

2. The conveying of angular increments by the modulator pulses.

3. The conveying of angular increments by the sinusoidally varied
pulse.

4. The method of phase-shifted pulses.

5. The conveying of sine and cosine by a-f signals of different fre¬
quencies.

Certain qualitative comparisons among these are possible.

The method of relaying angular increments by modulator-pulse timing
is by far the simplest if it can be used, which is only when the scanner
rotates very uniformly and can be exactly synchronized with the modu¬
lator. Unfortunately, the tests of this method were made in connection
with an airborne radar in which the scanning rate varied considerably;
hence appreciable inertia could not be used. Furthermore, multiple-
pulse coding had not been adopted at that time. As a result, interference
led to somewhat erratic results. Since no opportunity has arisen for
testing with a proper radar and with coded pulses, it is difficult to make an
accurate assessment, but the comparative success under unfavorable
conditions indicates that when properly applied the method can be
satisfactory.

If the scanning is fairly uniform but cannot be synchronized with the
modulator, the method of the sinusoidally varied pulse (Sec. 17-5) gives
very satisfactory results with a minimum of complexity as proved by a
reasonable amount of testing (Sec. 17-15). This method is somewhat less
susceptible to interference effects than Method 2 since more data are
sent per radar cycle and since an extra pulse does not cause an irreversible
effect.

The method of relaying sine and cosine data by pulse-timing tech-

Sec. 1710]

THE RADIATION PATH

713

niques has given satisfactory results even under very severe interference
conditions. It can, of course, follow sector, as well as continuous,
scanning. Its principal drawback is its relative complexity, but much
of the complication in Fig. 17-14 arises from extreme precautions against
interference and from the necessity of operating a servomechanism.
Were fixed-coil PPI’s used, or were it possible to operate a servomecha¬
nism satisfactorily from d-c signals, the equipment would be considerably
simplified. A far simpler model operating fixed-coil PPI’s and designed
for less severe interference conditions has seen considerable successful
service.

The phase-shifted pulse method is quite comparable to the sine-
cosine method in effectiveness; its method of converting to mechanical
motion is somewhat simpler, and it has considerably fewer adjustments.
Since more data are transmitted per radar cycle, greater protection against
interference is probably afforded. Although this method is of more
recent origin than the sine-cosine method, has not been so highly devel¬
oped, and has not had such thorough tests, it appears to be satisfactory.

The sine-cosine method using multiple a-f signals is in principle
quite simple and should prove satisfactory. Although it has been
successfully operated in an actual system (not at the Radiation Labora¬
tory), the author is not aware of any extensive tests in the presence of
interference. This method requires more complicated and wider-band
transmitting and receiving equipment than do the pulsed methods which
involve time sharing.

THE RADIO-FREQUENCY EQUIPMENT

In selecting the radio-frequency equipment, the requirements to be met
and the operational conditions must be carefully considered. Among the
important factors are the station locations (land-, water-, or air-based),
the maximum range required, the types of interference to be met, and the
nature of the data to be transmitted. These factors affect many of the
variables of the design, such as the types of antennas chosen, the r-f power
necessary, the carrier frequency most desirable, and the mechanical
construction of the equipment.

17-10. Antennas, Frequencies, and the Radiation Path. —The antenna
gain should be as high as practicable at both stations. For a given
transmitted power, the signal discernibility is always directly proportional
to the gain of the transmitting antenna. At the receiving station the
signal-to-internal-noise ratio is also proportional to the antenna gain,
and considerable interference reduction is accomplished by the direction¬
ality that accompanies high gain. Such antennas therefore permit the
use of much lower power to achieve a given result than would be required
with omnidirectional antennas.

Highly directional antennas can alw’ays be used for transmission

714

RADAR RELAY

[Sec. 1710

between fixed ground stations since they can be permanently oriented in
the correct direction. Very high, even microwave, frequencies are
desirable for such applications since directional antennas can then be
small, rugged, and easily constructed and installed. At least one micro-
wave equipment has been successfully used in experimental tests (Secs.
17-14 and 17-15).

When one or both stations are moving, on the other hand, it is neces¬
sary either to use sufficiently wide antenna patterns to provide coverage
in all the necessary directions, or else to provide for automatic pointing
of the antenna, with the consequent added complexity and weight. (If
several receiving stations are involved the transmitting antenna must
cover them all.) As a result, lower frequencies (100 to 900 Mc/sec) have
predominated in such applications since more power is available and
higher antenna gains can be obtained with a given pattern. In cases
involving transmission from aircraft, certain interference effects described
below are much less troublesome at low frequencies than at very high
frequencies.

In systems tested at the Radiation Laboratory for the transmission
of data from an aircraft to the ground, elementary antenna arrays have
been used. One system, operating at 300 Mc/sec, had a vertically
polarized dipole mounted on the tail section of the aircraft and two verti¬
cally stacked dipoles at the receiving station. The vertical gain of this
latter antenna improved somewhat the ratio of signal to inherent and to
local noise, but did not reduce interference appreciably since little inter¬
ference comes from high angles. In a test of a 100-Mc/sec relay equip¬
ment, the transmitting antenna was a quarter-wave vertical radiator
mounted on the skin of an aircraft and a corresponding vertical quarter-
wave receiving antenna was used at the ground station.

When a link was established at 800 to 900 Mc/sec, it was found very
desirable to increase the gain of the two antennas in order to extend the
usable range of the equipment. This was accomplished by using stacked
dipoles at both the transmitting and receiving stations. These arrays
had a uniform horizontal pattern and some gain in the vertical plane.

Associated or near-by equipments often constitute a serious source of
interference; consequently both antenna and power-line filters are desira¬
ble at the receiving station. Frequently these must be designed to reject
a particular frequency being radiated by a near-by antenna. Conversely,
it is often necessary to filter the r-f output of the relay transmitter in
order to minimize the radiation of harmonics that interfere with near-by
receivers. The specific filters required for a given installation must be
designed to meet the operational requirements of a specific system involv¬
ing a given complement of radar, communication, and navigational
equipment. No general rules can be given.

Sec. 1710]

THE RADIATION PATH

715

Diffraction Phenomena .—Whenever one of the relay stations is in an
aircraft, especially if the transmission path is over water, interference

Fig. 17-15. —Field intensity vs. range for propagation of vertically polarized signals
over sea water at various frequencies. Transmitter antenna height, 5000 ft; receiver
antenna height, 75 ft.

Range in nautical miles

Fig. 17T6.—Field intensity vs. range for propagation of vertically polarized signals
over sea water at various receiving antenna heights. Transmitter antenna height, 5000 ft;
frequency, 300 Mc/sec.

between direct and reflected rays can occur. This subject is treated
in detail in Yol. 13 of this series. Figure 17-15 shows curves of

716

RADAR RELAY

[Sec. 17-10

signal strength as a function of range for frequencies of 100, 300,
and 850 Mc/sec, displaying the effect of frequency on the number and
the magnitude of the fluctuations in signal strength that are due to
interference. Figure 1716 shows curves of signal strength as a
function of range for receiver antenna heights of 75, 110, and 140 ft
above the surface of the sea. These curves indicate the manner in which
the effects of signal cancellation can be reduced by using diversity recep¬
tion with antennas at different heights. A simple diversity system might
consist of two antennas respectively 75 and 140 ft above the sea, with
arrangements for switching the receiver to the antenna providing the
greater signal strength at any given moment. In effect, this reduces the
depths of the cancellation minima in either of the antennas considered
separately.

Future Trends in Frequency .—Frequencies most generally used for
radar relay have been in the region from one to a few hundred megacycles
per second, partly for reasons of achievable power, higher gains of non-
directional antennas, and so on. Future trends appear to lead toward
higher frequencies, up to and including microwaves.

Comparatively speaking, the use of such frequencies is characterized
by the possibility of using simple, highly directional antennas, by low
gain in omnidirectional antennas, by reduction in man-made static
(except for pulse interference from radars), by a great increase in the
overwater diffraction effect, by a large number of available channels, and
by the relatively low power now available for c-w operation.

The powers available for continuous operation with equipment devel¬
oped by the end of the war are approximately as follows:

100 Mc/sec

(FM).

(AM).

300 Mc/sec

(FM).

(AM).

1000 Mc/sec
(FM).

(AM).

3000 Mc/sec (FM).
10,000 Mc/sec (FM)

100 watts average
100 watts average
250 watts peak video level
500 watts peak in pulses

30 watts average
30 watts average
80 watts peak video level
175 watts peak in pulses

25 watts average

( 25 watts average
40 watts peak video level
80 watts peak in pulses
10 watts average
0.1 watts average

Any of these is sufficient for use in applications where both antennas
can be directive, and there is little question that the very highest fre-

Sec. 17-11]

GENERAL EQUIPMENT CONSIDERATIONS

717

quencies will be used for such purposes in the future. Until recently it
was not economical to use a-f modulation of microwaves because of the
extreme oscillator-stability requirements necessary to avoid excessive
bandwidth. However, a highly ingenious application of a microwave
discriminator in combination with a feedback amplifier controlling the
oscillator frequency 1 appears to overcome this difficulty and to permit
the use of c-w synchronization methods.

For applications requiring omnidirectional antennas, the ranges so far
obtained at frequencies above 300 Mc/sec have been rather limited, espe¬
cially in situations involving diffraction effects. As greater power becomes
available at the higher frequencies, they will undoubtedly find more and
more applications even where it is not possible to use highly directed
beams. The diffraction difficulty can largely be overcome by the careful
use of diversity antennas.

17-11. General Transmitter and Receiver Considerations. —Although
the specific characteristics desirable in the transmitter and receiver
depend upon the particular application, certain general statements can be
made.

The transmitter should provide sufficient power to ensure clear signals,
free from noise and interference, at the maximum required range. In
common with all components, it must have sufficient bandwidth to accom¬
modate the band of frequencies present. The receiver should have a
satisfactory noise figure, a proper bandwidth, and in many cases must
provide special means of distinguishing between desired and undesired
signals by methods analogous to the antijamming techniques described
in Sec. 12-8. Automatic gain control is necessary to prevent strong
signals from overloading the receiver, and to insure that signals are
applied to the decoder at the correct level.

Bandwidth varies with the particular characteristics of the radar set
and the type of synchronization used. In general, the video sections will
have a bandwidth between 1 and 3 Mc/sec, with corresponding r-f and
i-f bandwidths from 2 to 6 Mc/sec, when normal search radar systems are
used. Since the relay link is only one section of the over-all channel, the
bandwidths of its components must be somewhat greater than would be
necessary if it alone were involved.

An important decision is the choice between amplitude and frequency
modulation. The relative advantages and disadvantages of these two
methods are somewhat different for pulsed and for c-w signals, and
depend also upon the type of interference expected. The principal
advantage of frequency modulation is this: if the carrier power is appreci¬
ably greater than that of an interfering signal, the latter tends to be

1 R. V. Pound, “An Electronic Frequency Stabilization System for Cff Micro-
wave Oscillators,’’ RL Report No. 815, Oct. 1, 1945; Rev. Sci. Inst. 17, 490 (1946).

718

RADAR RELAY

[Sec. 17-11

suppressed. Frequency modulation is thus helpful in cases where it is
desirable to remove the last traces of low-level interference. Such inter¬
ference reduction is effective only if a large deviation ratio is used, that
is, if the ratio of half the maximum carrier-frequency excursion to the
maximum modulation frequency is large. (A deviation ratio of 4 is
considered excellent.) This requirement increases the necessary band¬
width of the r-f parts of the transmitter, and of the r-f and i-f stages of
the receiver. This increase presents additional transmitter circuit prob¬
lems, and reduces the gain in the amplifier stages. In the receiver, the
greater bandwidth admits more interference in addition to complicating
the receiver design.

The most important aspects of the relative virtues of the two types of
modulation arise, however, in connection with the consideration of
particular types of signals and interference. For example, if pulse
synchronization signals are received at a level appreciably above that of
interference, amplitude-selection methods can entirely exclude the inter¬
ference, regardless of the type of modulation. This gives the amplitude-
modulation method a definite advantage because the low duty ratio of
the synchronization pulses makes it possible to transmit them at peak
powers several times higher than the permissible average 1 and thus
assists these signals to override the interference. A fairly high ratio of
peak to average power can also be maintained for video signals since,
except in extreme cases, echoes are received for only a small fraction of the
time. In frequency modulation, on the other hand, the carrier operates
at a constant power level.

No such advantages exist for amplitude modulation in connection with
c-w synchronization methods. Low-level, more or less continuous
interference can be very disturbing, and the natural suppressing effect of
the limiter and discriminator in an f-m receiver can be of very great
advantage. Furthermore, the use of subcarriers and carriers of higher
order can be most readily accomplished in a system which is frequency-
modulated throughout.

The above discussion, admittedly rather hypothetical in the absence
of extended comparative tests, might be summarized as follows:

1. Amplitude modulation methods seem preferable for the relaying
of synchronization pulses (of which there is always at least one),
the advantage increasing with the strength of the interference.

2. There is probably little to choose between AM and FM with
respect to the video signals. If the interference is severe, the
higher peak powers and narrower bandwidths possible with ampli-

1 This is usually accomplished by combining grid modulation by both the video
and the pulse signals with plate modulation by pulses only.

Sec. 17 - 12 ]

300 -MC/SEC A-M EQUIPMENT

719

tude modulation make it preferable; if, on the other hand, the
interference is at low level it can be more completely suppressed
by frequency-modulation methods.

3. Frequency-modulation methods are definitely preferable for c-w
synchronization signals.

The following sections give brief descriptions of some actual equip¬
ments.

17*12. A 300-Mc/sec Amplitude-modulated Equipment. —Largely
because of its availability, the type of r-f equipment most used at Radia¬
tion Laboratory consists of a modification of an amplitude-modulated
television transmitter-receiver combination operating in the 300-Mc/sec
region (specifically on any of 10 channels between 254 and 372 Mc/sec).
The transmitter provides 90 watts of peak video signal power, and 250
watts of pulse power.

A block diagram of the transmitter is shown in Fig. 17T7a. Provi¬
sion is made for grid modulation by all of the signals and for additional
plate modulation by synchronization pulses. Negative video and syn¬
chronization signals are amplified by a three-stage broadband video
amplifier. The second stage has a gain control in the cathode to compen¬
sate for variations in input-signal amplitude. The amplified signals drive
the grids of the 8025 r-f power amplifiers through a cathode follower.
Since the bias for the cathode follower must remain constant for all duty
ratios, a d-c restorer is used between its grid and the — 105-volt supply.
The synchronization pulses are amplified by a 4-stage video amplifier oper¬
ating into a pulse transformer connected to the cathode of a diode through
which the r-f amplifiers draw their power. In the absence of pulses, the
diode is conducting and the plates of the r-f amplifiers are connected to
the high-voltage supply (800 volts). The arrival of a pulse disconnects
the diode and raises the plate potential of the amplifier by several hundred
volts, resulting in a very high instantaneous power.

The master oscillator consists of a pair of 8025’s in push-pull, the plate
and grid circuits being tuned by transmission-line elements of variable
length. The amplitude of oscillation is controlled by the capacitive
reactance of the filament line, and can also be varied by changing the
length of the filament line. -Change of channel necessitates retuning of
the r-f power amplifier by adjustment of a short-circuiting bar on the
parallel line which constitutes the plate load. The electrical length of
the coupling loop is also varied with the plate tuning. The monitor
diode rectifies a small portion of the output signal, which is displayed on a
scope for monitoring purposes.

A reflectometer, or bidirectional coupler, is coupled into the r-f line
at all times. This gives a continuous indication of the power output and

720

RADAR RELAY

[Sec. 17-12

provides a means of measuring the standing-wave ratio on the line. The
bidirectional coupler consists of a short section of line in which is mounted
a directional pickup loop. At orientations 180° apart, the loop picks up

(a) Transmitter

interference suppression

(b) Receiver

Fig. 17-17.—300-Mc/sec amplitude-modulated equipment.

the outgoing power and the reflected power respectively. The filter
section is installed to prevent radiation of harmonics and other spurious
off-frequency signals. It has been designed to have 50 ohms impedance,

Sec. 17 - 13 ]

100 -MC/SEC F-M EQUIPMENT

721

an insertion loss of less than 2 db from 290 to 320 Mc/sec, and a loss of
more than 40 db above and below this band. The design is conventional:
three T-scctions are matched to the line with a ir-section at each end.
Inductors are used as series elements, and combinations of lines as the
shunt elements.

Figure 17-176 shows a block diagram of the receiver. The r-f ampli¬
fier is a miniature triode (6J4) connected as a grounded-grid amplifier. A
dual triode (6J6) is used in a push-pull oscillator circuit tuned 30 Mc/sec
below the carrier frequency. The 30-Mc/sec i-f signal from the converter
is amplified by six stages, gain control being applied to the first three.
The i-f bandwidth is about 3 Mc/sec between half-power points. The
output of the detector, a 6AC7 connected as a diode, is applied to the first
video stage. A choice of two time constants is available in the grid
circuit of this stage, 0.47 sec and 2.4 ^sec. The longer one is normally
used; it gives good response to very low video frequencies. The short
time constant, when used, serves the same function against extended or
c-w interference as similar circuits do in a radar receiver (Sec. 12-8).

The automatic gain control is actuated by the synchronization pulses.
A small signal is taken from the plate of the final cathode follower,
amplified, and passed to another cathode follower. Because of inverse
feedback, the output signal of this cathode follower is a sharp spike,
rather than a flat-topped 2-^sec pulse. If the synchronization pulses are
coded, they pass through a delay line to a coincidence tube, the com¬
bination acting as a decoder. The coincidence tube is so biased that only
pulses will actuate it, the video signals being biased out at this point by
the video-level control. The output signal of the coincidence tube is
applied to the cathode of a diode, whose plate potential is set by the AGC
level control. Thus, if the signals from the coincidence tube are suffi¬
ciently negative to cause the diode to conduct, the grid of the cathode
follower which is also connected to the plate of the diode will change
potential and thereby change the grid potential on the first three i-f
stages. A long time constant in the cathode-follower grid circuit holds
the grid potential essentially constant between pulses. There is thus a
loop in which strong pulses produce a more negative potential on the i-f
grids to reduce the receiver gain, and vice versa.

It may happen that operation of a radar in the vicinity will overload
the receiver during transmission. Such interference can be overcome
by introducing a portion of the interfering radar trigger at the interfer¬
ence-suppression terminals shown. This reduces the receiver gain at the
instant of radar transmission, with the loss of only one or two microseconds
of video-signal reception.

17-13. A 100-Mc/sec Frequency-modulated Equipment. —A second
type of equipment which has been used for air-to-ground or air-to-ship

722

RADAR RELAY

[Sec. 1713

relay links is a 100-Mc/sec frequency-modulated system. The equip¬
ment operates at four frequencies between 78 and 116 Mc/sec, channel¬
changing being accomplished in the receiver by a coil-switching mechanism
and in the transmitter by plug-in coils. A block diagram is given in
Fig. 1718. The input signals are amplified and delivered push-pull to
the deviator by a phase splitter. The deviator acts as a reactance tube,
modulating an oscillator which operates at one-eighth the desired carrier
frequency. Three stages of frequency-doubling and power amplification

Receiver

Fig. 17-18.—100-Mc/sec frequency-modulated equipment.

follow. The final stage consists of a pair of 4E27 tubes operated as a
Class C amplifier with an average r-f output power of about 100 watts.

The equipment is designed to accommodate a maximum video
bandwidth of 2 Mc/sec. The oscillator gives a maximum linear fre¬
quency deviation of 0.5 Mc/sec. Therefore, in this and the first doubler
stage the bandwidth need be only the 2 Mc/sec determined by the
video frequencies involved. After a second doubling, the bandwidth
is made 4 Mc/sec in order to support two sidebands on each side of
the carrier. After the final doubling, a bandwidth of 6 Mc/sec would be
required to support all the sidebands above 5 per cent, but it was found
experimentally that distortion was not serious if the bandwidth were
reduced to 4 Mc/sec. This simplified the amplifier design and resulted in
higher r-f power than would otherwise have been available.

Sec. 1714] MICROWAVE SYSTEM FOR POINT-TO-POINT SERVICE 723

Two miniature double diodes are included in the transmitter for
monitoring purposes. One of these tubes is connected as a discriminator
to provide a video-output test point at the antenna-line connector. Dur¬
ing all testing, this video signal gives an accurate over-all check of the
r-f and video sections of the transmitter. One half of the remaining
double diode is used as an r-f detector to provide a relative power indica¬
tion on a panel meter which is also used, by means of a rotary selector
switch, to measure the grid currents of the several doublers. This diode
is also connected to a test point to allow a scope to be used when over-all
alignment and bandwidth measurements are being made. Because of
the stability of this transmitter, it was found unnecessary to use a bidirec¬
tional coupler with it.

The receiver has one tuned r-f stage, a mixer, a local oscillator, seven
i-f stages, two limiters, a discriminator, a video amplifier, and three
tubes connected in parallel as a cathode-follower output stage. All the
tubes in this section of the receiver are 6AK5 miniature pentodes, except
the one used in the discriminator which is a 6AL5 miniature double diode.

The r-f, i-f, and video sections, as well as the discriminator, are stand¬
ard in design, an 8-Mc/sec bandwidth in the i-f amplifier being obtained
by double staggering of alternate stages. A two-stage limiter is used to
insure constant input-signal voltage at the discriminator. Both limiter
tubes operate at reduced plate and screen voltages to reduce the grid
swing necessary to cause plate limiting. A fast time constant in the grid
circuit of the first limiter was chosen to discriminate against impulse
noise by producing the limiting bias quickly. Longer time constants are
possible in the second limiter since the signal variations at this tube are
neither large nor of short duration.

This equipment has been given extensive airborne tests in conjunction
with two different types of synchronization equipment, and has also been
operated between fixed ground stations.

17*14. Microwave System for Point-to-point Service. —The two
equipments described in Secs. 17-12 and 17-13 were developed primarily
for air-to-surface work involving the use of omnidirectional antennas; an
upper limit was therefore set to the possible radio frequency. The pres¬
ent section will describe equipment designed for use between fixed ground
stations which permit the use of directional antennas.

Safe margins of power are easily attainable in such applications since
the maximum range is usually sharply limited by the horizon or by rough¬
ness of the terrain. The received signal was specified to be 40 db above
thermal noise at maximum range in order to provide a safe operating
margin. In the application of this criterion to the selection of frequency
and antenna sizes, the following table is illuminating. Paraboloid
antennas are assumed at both stations.

724

RADAR RELAY

[Sec. 17-14

Table 17-1.— Maximum Range of Relay Systems

Frequency,

Mc/sec

Power,

watts

Beamwidth, degrees

Free-space range, miles

9-ft

paraboloid

3-ft

paraboloid

9-ft

paraboloid

3-ft

paraboloid

300

« 27

« 80

196

1,000

460

3,000

2.7

195

10,000

0 1

0.8

2.4

292

32.5

When one considers the power involved, the decrease of man-made
interference with increased frequency, and the privacy and protection
from interference provided by narrow beams, microwave frequencies
appear to be the most desirable. The decision between 3000 and 10,000
Mc/sec was based largely upon the fact that in the latter case waveguide
of a convenient size could be used, an extremely desirable design feature.
Since a 32-mile range is adequate for the uses intended, and since too
great sharpness of beam might lead to alignment difficulties, 3-ft parabo¬
loids were used at both stations.

Frequency modulation was chosen, partly because of its advantages
when signal-to-noise and signal-to-interference ratios are high, but mostly
because it simplified the oscillator design. Large deviations of the oscil¬
lator are easily accomplished, and there are no problems of r-f bandwidth.
Since the required video bandwidth was about 1.5 Mc/sec, a total
deviation of 6 Mc/sec was chosen. The total frequency spectrum
involved is then a little more than 9 Mc/sec. In order to minimize the
required i-f bandwidth in the receiver, the discriminator was set on one
side of the pass band of the receiver. A value of 11 Mc/sec was then
chosen for the i-f bandwidth to provide a margin to take care of improper
tuning.

The equipment is shown schematically in Fig. 17-19. The oscillator, a
2K39 reflex klystron, is stabilized against a cavity by means of a microwave
discriminator. 1 The output of this device is a d-c signal whose voltage is
proportional to the deviation of the oscillator frequency from the fre¬
quency for which a resonant cavity, used as comparison standard, is set.
This error signal is amplified by a push-pull d-c amplifier and used to
control the reflector voltage of the klystron in such a way that its fre¬
quency is forced into agreement with the resonant frequency of the cavity.
Video signals and pulses are applied directly to the reflector to produce
the desired frequency modulation. Rapid response is purposely avoided

1 R. V. Pound, A Microwave Frequency Discriminator, RL Report No. 662,
Aug. 4, 1945; Rev: Sci. Inst. 17, 490 (1946),

Sec. 17-14] MICROWAVE SYSTEM FOR POINT-TO-POINT SERVICE 725

in the frequency-control circuits so that they will not stabilize against the
signal frequencies.

Not shown in the transmitter diagram is a monitor, consisting of a
crystal mixer and a video amplifier, which draws power from the main
waveguide. In combination with a synchroscope, this provides a very
effective means of checking and aligning the transmitter.

Reference

Fiq. 17’19.—Microwave equipment.

The local oscillator of the receiver is also frequency-stabilized against
a cavity. The circuits and layout of the i-f amplifier and the automatic
gain control are similar to those of the receiver described in Sec. 12-11,
the bandwidth being 11 Mc/sec. A two-stage limiter is used ahead of the
i-f discriminator, care being exercised to provide sufficiently rapid limiting
action to reduce impulse noise. The discriminator is similar to that used
in radar AFC circuits and has a bandwidth of about 17 Mc/sec between
peaks.

726

RADAR RELAY

[Sec. 17-15

RADAR RELAY SYSTEMS

Two complete radar relay systems will now be described; their general
features are sufficiently applicable to future requirements to make this
worth while, even though better systems could now be designed. The
requirements for the two systems are quite different. The first involves
the transmission between fixed ground stations of three sets of radar echo
signals and one set of beacon signals, all resulting from antennas mounted
on a single continuously rotating scanner. Although the number of sets of
video signals is large, the use of directional antennas eases the r-f problem,
and the continuous scan renders scanner synchronization relatively
simple.

In the second example, one set of radar signals and one set of beacon
signals are relayed to ground from a long-range airborne radar set
arranged to permit sector scanning. In contrast to the former case, the
“picture” data are relatively simple, but the requirement of large
angular coverage forces the use of low-gain antennas and puts a severe
requirement on the r-f system. Sector scan and the turning of the
aircraft greatly complicate the scanner-synchronization problem.

17-15. A Ground-to-ground Relay System. —The radar set originat¬
ing the data in this example is a ground-based microwave set (see Chap.
15) in which the scanner, rotating at either 2 or 4 rpm, carries two
radar antennas and one beacon antenna. One of the radar antennas pro¬
vides long-range low-angle coverage; the other provides coverage at high
angles. Both regular video signals and MTI (Chap. 16) video signals are
derived from the upper-beam signals; this beam is chosen for MTI because
it is the one predominantly used at the shorter ranges where the clutter is
worse.

Thus four sets of video signals must be transmitted: lower-beam
radar echoes, upper-beam radar echoes, upper-beam MTI video signals,
and beacon responses. Time sharing is used to put two sets of video
signals on each of two carriers. One channel is shared between the MTI
video signals and the lower-beam video signals, MTI video being trans¬
mitted for a time interval corresponding to the first 30 to 50 miles of
range from the radar, and the lower-beam video for the remainder of the
radar cycle. A second channel is shared between the upper-beam radar
echoes and the beacon signals; since the data from these two are simul¬
taneous, switching must be done on a whole-cycle, rather than on a frac¬
tional-cycle, basis. Two pulse cycles are allotted to radar, then one to
beacon, and so on, the unequal division being used because signal sensi¬
tivity is more critical in radar than in beacon operation. The resultant
loss in sensitivity is 0.5 db for radar signals and 1 db for beacon returns.

Two transmitters, feeding a common antenna through a duplexer, are

Sec. 17-15]

A GROUND-TO-GROUND RELAY SYSTEM

727

used to provide the two channels, since, at the time of design, equipment
accommodating subcarriers was not available and weight and power were
not crucial items. The remaining data are combined on these same two
channels as indicated in Fig. 17-20. The mixing and switching of the
signals for the first transmitter is fairly simple. Range markers and the
proper set of angle markers are mixed with each set of video signals, and
the two sets are fed to a video switch, which passes the MTI signals for
the first 50 miles or so and the lower-beam signals thereafter. The
switch is like the circuit of tubes Vu and Vu of Fig. 17-3, but has signals
on both grids.

The synchronizer is similar in function to that of Fig. 17-5 (including
Fig. 17-2), 1 with the addition of a scale-of-three circuit to produce the
beacon switch pulse on every third cycle. The third pulse of the mod¬
ulator code is counted down for this purpose and passed to the signal
switching unit. The switching signal to be relayed is delayed 16 ^sec (by
reflection in an 8-Msec delay line) in order that it be clear of the azimuth
pulse at the receiving station. 2 The three-pulse code, the azimuth pulse,
and the beacon pulse are “mixed” by using them all to trigger a blocking
oscillator.

The video signals to the second transmitter are switched twice.
The upper-beam video and the beacon video are switched cyclically as
described above. The switch is controlled by a flopover circuit (Fig.
13T6) which remains in the stable state that causes video switch a
to pass the radar signals until a beacon switch-pulse occurs; it then passes
to a second stable state that causes the video switch to pass beacon
signals. At the next modulator pulse the original condition is restored.

A video switch provides for time sharing between the video signals
and the synchronizing pulses in order that the former shall not interfere
with the latter. In its normal position, the flip-flop holds switch b in
the state that passes pulses. Firing of the flip-flop by a pulse delayed by
30 Msec from the modulator pulse reverses the video switch allowing echo
signals to pass. The flip-flop returns spontaneously to its original state
shortly before the start of the next radar cycle. Signals from switch b
are combined with range and angle marks in a video mixer, from which
they pass to transmitter No. 2.

At the receiving station, the signals pass through a duplexer to two
receivers. The first delivers the time-shared MTI and lower-beam video
signals, together with markers, directly to the indicators. Signals from

1 The circuit details of the equipment actually tested differ considerably from
those of Figs. 17-2 and 17-5.

2 In order that pulses passing through the three-pulse coincidence circuit shall not
cause false coincidences, they should follow each other by at least the sum of the code
length and the pulse length—in this case a total of 8 Msec.

728

RADAR RELAY

[Sec. 17-15

Modulator

pulse

|—— 3300^ see —[_|_[_

J I_! I_I I_I L.

--MTI -■ Lower—>—-MTI-»-—Lower- » - MTI*—Lower—--MTI—Lower—MTI
beam beam beam beam

Expanded

time

__^

300sec

J- L

“H 1 1.

-*l 3000/< sec b-

iii ii __*. iiiii

111_-

_Hi! jUH: _ >Wi III 1

Beacon video

1 1 1

Radar video

Radar video Beacon video

_i_L_a—__

scale

0 2 6

30/r sec

Modulator pulse

Azimuth

Beacon

Video switch Video

code

pulse

signal

pulse

1 1

1 _

1 I

N .

Fio. 17-20.—Ground-to-

Sec. 1715]

A GROUND-TO-GROUND RELAY SYSTEM

729

ground radar relay.

730

RADAR RELAY

[Sec. 17-15

the second receiver contain the coded modulator pulse, the azimuth pulse,
and the beacon switch pulse. They pass through a switch which excludes
all signals while video is being transmitted but opens shortly before the
arrival of a trigger pulse. This switching, the decoding of the modulator
pulse, and the derivation of the scanner information from the azimuth
pulse, are done by methods similar to those of Figs. 17-2 and 17-5. The
upper-beam video signals and the beacon video signals are separated by a
video switch which consists essentially of a pair of out-of-phase switches
similar to that made up by tubes Vi a and Fn in Fig. 17-3. The video
switch is controlled by a flopover which is triggered to the beacon position
by the beacon switch pulse and to the radar position by the next modula¬
tor pulse. The switch pulse is singled out by coincidence with a pulse
derived locally (N) at the proper time by delaying the decoded modulator
pulse.

The time occupied by the pulse code results in the triggering of the
indicators 8 /isec too late. This produces a slight distortion in the dis¬
plays, but there is no error in range measurements since accurate range
markers are transmitted with the video signals. The display distortion
is unimportant because short-range displays are not used. Similarly, the
fact that the indicators must be blanked out for the first 30 nsec is of no
importance since targets at such close range are practically never of
interest.

Several r-f equipments, including the three described in earlier
sections, were tried experimentally in this application. All operated
with reasonable satisfaction, maximum range being limited in every case
only by the line of sight. On the whole, the microwave equipment is
considerably superior to the others because of its compactness, the small
power involved, the narrowness of the beam, and the greater freedom
from interference. However, the fact that the use of frequency modula¬
tion did not permit the pulses to be transmitted at higher level than the
video signals was a definite handicap for reasons described below.

The equipment as a whole operated about as anticipated. Compara¬
tive PPI photographs taken simultaneously at the two stations are shown
in Fig. 17-21. The only difficulties of consequence involved occasional
loss of synchronization, usually because of pulse interference picked up
on the radio link or on the radar set. The direct results of spurious
triggers on either the angle data or the sweep triggering were not appreci¬
able, but loss of the trigger occasionally upset the sequencing with
unfortunate results. Once the proper chain is broken, it can be spuriously
started by interference or by video signals and remain in error for several
cycles. Both the indicator sweeps and the azimuth data are then in
error, sometimes by as much as 5° or 10°. The resulting angular error
persists until it is manually removed. When amplitude selection of the

Sec. 17-16J

A QROVND-TO-GROUND RELAY SYSTEM

731

Fig. 17-21. —Comparative PPI photographs taken simultaneously at the transmitting and
at the receiving stations.

732

RADAR RELAY

[Sec. 17-10

pulses is possible (with the amplitude-modulated equipment), these
effects are greatly reduced. Amplitude selection also provides suppres¬
sion of weak interference picked up on the link itself. With this pro¬
tection interruptions are extremely brief and cause little difficulty.

17*16. Relay System for Airborne Radar. —In the system just
described, the scanner synchronization was rendered fairly simple by the
continuous scanning, and the problem of obtaining adequate signal
strength was simplified by the use of directional antennas. The principal
complications were those involved in the simultaneous transmission of
several sets of video data. The present section will describe briefly
the arrangements used to solve a far more difficult problem, in which the
data originate from a long-range airborne set equipped for sector scanning.
The scanner synchronization, difficult in any case, is rendered far more
so by the fact that the omnidirectional antennas required give so little
gain that the interference problem is severe. Every possible device must
be used to provide a maximum of power from the transmitter, to reject
interference in the receiver, and to protect the synchronization pulses by
coding, by switching, and so on.

The video data involved are simple, consisting merely of radar signals
and of signals from a separate beacon receiver. In order that the two
sets of video signals may be accommodated, cyclical time sharing is used
during the intervals of beacon use, the modulator trigger serving as the
signal that radar is being transmitted on a given cycle.

The design was built around the sine-cosine synchronization method
of Sec. 17-9 and the 300-Mc/sec amplitude-modulated r-f equipment of
Sec. 17-12. Much experimentation was done, however, with the phase-
shifted pulse method of synchronization (Sec. 17-6), and with the
100-Mc/sec frequency-modulated r-f equipment of Sec. 1713. The
former combination is outlined in Fig. 17-22, in which some parts peculiar
to this system and not heretofore described are shown.

It is necessary to provide the azimuth data in terms of compass
directions rather than aircraft heading. To accomplish this, an a-f wave
is passed through a two-phase synchro on the scanner and a two-phase
differential synchro controlled by a compass so that the two resulting
signals have amplitudes proportional to sin 6 and cos 6 respectively,
where 0 is the scanner orientation with respect to true north (See. 13-4).
Each of these signals is passed through a phase-sensitive rectifier keyed
by the audio oscillation in order to develop the slowly varying voltages
necessary to control the sine and cosine delay circuits (Sec. 17-8).

The remainder of the synchronizer is like that shown in Fig. 17-14
except for the provision for radar-beacon switching on alternate cycles.
During periods of beacon use, the relay of Fig. 17-14 is to the right,
diverting the modulator pulse from the coder to the scale-of-two multi-

Sec. 17-16]

RELAY SYSTEM FOR AIRBORNE RADAR

733

vibrator of Fig. 17-22. The square waves from the latter control a
switch that alternates between radar and beacon video signals, if the
latter are to be relayed. A pulse formed on those cycles in which radar is

_ Analyzer and_scan converter___I

Fig. 17-22.—Air-to-surface relay system.

transmitted is passed to the coder to serve as an identifying pulse in the
relay channel. When the beacon signals are not desired, the relay of
Fig. 17-14 is reversed and the original pulses go to the coder on every
cycle.

734

RADAR RELAY

[Sec. 17-16

The video switch of Fig. 17T4 alternates the video signals (radar or
radar alternated with beacon) with the coded pulses, and passes the
results to the transmitter (Fig. 17-22), where they ultimately modulate
the grid of the r-f power amplifier. The pulses are additionally used to
modulate the plates of the same tubes; this arrangement provides a much
higher power in the pulses than would otherwise be available. The
transmitter power is approximately 50 watts average, 80 watts peak on
video signals, and 175 watts peak on pulses.

An r-f filter is provided in the antenna lead. The antenna consists
of a vertically polarized dipole mounted on the tail section of the aircraft.

At the receiving station, the energy is received by an antenna con¬
sisting of two vertically stacked dipoles and passes through a resonant
cavity of loaded Q equal to 100 on its way to the receiver described in
Sec. 17-12.

The analyzer and scan converter operate as shown in Fig. 17-14,
separating the various signals and providing a simulated scanner motion.
The separation of video signals from pulses is aided by an amplitude
selector which takes advantage of the higher power in the pulses. This is
helpful, especially during the locking-in period. The additional parts
necessary to separate the radar and beacon data are shown in Fig. 17-22.
The cosine pulse is delayed 30 jusec to form a trigger available on every
cycle, regardless of whether radar or beacon video signals are being
transmitted. The modulator pulse indicates those cycles on which radar
video is transmitted. A trigger occurring only on the beacon cycles
can be formed by an anticoincidence circuit operated by these two pulses.
The video switch separating the two types of video is controlled by a
flopover which is thrown to the radar position whenever the modulator
pulse occurs, and back to the beacon position by the next cosine pulse.
The switch then passes beacon signals on every cycle in which the modu¬
lator pulse does not occur.

This equipment gave reasonably satisfactory results in its final form.
In spite of all the precautions taken, however, the considerable interfer¬
ence from radar and communications equipment, together with the
presence of diffraction minima, limited the reliable operating range to
about 30 miles when the interference was severe, and to 50 miles or so
under reasonably favorable conditions. These figures would be some¬
what improved by the use of diversity antennas, but in the absence of
tests no figures can be given.

Extensive tests of the 100-Mc/sec frequency-modulated equipment
have been made under less severe interference conditions than those
faced in tests of the 300-Mc/sec equipment. At 100 Mc/sec, diffraction
minima occur only at short ranges where the signal strength is high, and
they are much less pronounced than those at higher frequencies, as

Sec. 1716]

RELAY SYSTEM FOR AIRBORNE RADAR

735

indicated by Fig. 1715. This relative freedom from diffraction effects,
together with the higher antenna gains, gave the 100-Mc/sec equipment
better performance in the absence of severe interference than that of the
300-Mc/sec system. Under the test conditions, satisfactory results
were achieved at ranges up to 100 miles with the airplane flying at
10,000 ft. However, a great deal of interference exists in this frequency
band in busy locations. The tests did not give adequate opportunity
to observe the effect of this interference in reducing the maximum range
since the sites used were relatively isolated.

The phase-shifted pulse method of synchronization (Sec. 17-6)
gave results comparable to those of the sine-cosine method with either
type of r-f equipment under reasonably interference-free conditions.
Since it is slightly simpler and has fewer adjustments, it was therefore
somewhat superior under the test conditions. No data are available
on its relative performance in the presence of severe interference,

Index

Absorbent materials, 69
Absorber, of second kind, 69
Absorbing material, bandwidth of, 71
Absorption, atmospheric, effect of, 112
of microwaves, in oxygen, 59
in water vapor, 59
AFC, 453-457
beacon, 456
radar, 454-456
AI, 200

AI Mark IV, 201
AIA, 203

Air control, high-performance radar for,
592-611

Air surveillance, high-performance radar
for, 592-611

Aircraft electrical systems, 555
Aircraft interception (see AI)

Aircraft Radio Laboratory, 15
Airways, 574

Alternator, airborne, direct-driven, 557-
561

wave shape of, 557

aircraft, alternatives to direct-driven,
560

inductor, performance of, 557
voltage regulators for (see Voltage
regulators)

(See also Motor-alternator)
Altimeter, radio, 143-147
Altitude signal, 88
Alvarez, L. W., 291
A.M.E.S., Type 7, 186
Type 13, 190
Amplified back-bias, 459
Amplifier, gated, 508-510
i-f, 8

design of, 442-449
double-tuned, 446
single-tuned, 445

Amplifier, negative feedback, 492
phase-splitting, 495
squaring, 497

two-channel, for MTI, 672-675
video, 8, 450-453

cutoff frequency of, 451
rise time of, 450
Amplitude factor, 557
Amplitude modulation (see Modulation,
amplitude)

AN/APA-15, 306
AN/APG-1, 202
AN/APG-2, 202
AN/APG-15, 206
AN/APQ-7 scanner, 291-295
AN/APS-3, 199
AN/APS-4, 199
AN/APS-6, 203
spiral scanner, 290

AN/APS-10, detailed design of, 616-
625

detailed specifications of, 619
general design of, 614
performance of, 622
scanner, 288
units of, 618
AN/APS-15, 199
Angle indices, 514-518
fixed electronic, 514
movable electronic, 516
AN/MPN-1 (see GCA)

Antenna, beamwidth of (see Beamwidth)
cosecant-squared, 23-27
end-fire, 277

gain of (see Gain, of antenna)
mechanical construction of, 279-280
nonscanning, 277-279
paraboloid, 272-274
polyrod, 278
for radar relay, 713-719
receiving cross section of (see Cross
section, effective receiving)

737

738

RADAR SYSTEM ENGINEERING

Antenna, rolled parallel-plate scanning,
304

Schwartzsehild, 295-298
of SCI height finder, 298-302
stabilization of (see Stabilization; Sta¬
bilizer)

Yagi, 277

Antenna equation, 271-272
Antenna feed, 272-274
Antenna filter for radar relay, 720
Antenna mount, 271

Antenna pattern for airborne ground-
mapping, 23

Antenna temperature, 32
Anticlutter circuits, 460
Antijamming, 457-460
AN/TPG-1, 210, 211
AN/TPS-10, 191
antenna mount of, 286
Array, corrugated coaxial line, 303
of polyrod radiators, 303
A-and-R-scope, 166
ASB, 197
A-scope, 164
design of, 524-528

ASD, 199
ASD-1, 199

ASE, 196

ASG, 199

ASH, 199

Aspect function, 88
ASV Mark II, 196
ATR switch, 7, 407-111
ATR tube, 407

Attenuation, by fog or cloud, 60, 62
of microwaves in atmosphere, 58
by rain, 61
by water droplets, 60
in waveguide (see Waveguide, attenua¬
tion in)

Aural detection (see Detection, aural)
Automatic frequency control, 453—457
(<See also AFC)

Autosyns, 487

Azimuth-pulse removal, 695
B

Back-bias, 459

Back bombardment of magnetron cath¬
ode (see Magnetron cathode, back
bombardment of)

Back-of-the-dish system (see System,
back-of-the-dish)

Baltzer, 0. J., 80
Bandwidth, i-f amplifier, 444
over-all, of cascaded double-tuned
circuits, 448

of cascaded single-tuned stages, 446
of receiver (see Receiver bandwidth)
Bartelink, E. H. B., 449
Beacon, airborne, 246
azimuth width of reply of, 256
choice of frequency for, 260
fixed ground, 248
with ground radar, 609
interrogation of, 252-260
interrogation coding of, 263-264
frequency, 263
pulse length, 263
multiple pulses, 263
two-frequency interrogation, 264
overinterrogation of, 265
portable, 249
radar, 27, 243-270
general description of, 243-246
use for communication, 244, 264
range performance of, 254
reply coding of, 264
gap coding, 264
range coding, 264
width coding, 264
side-lobe interrogation of, 257
swept-frequency, 262
traffic capacity of, 265-268
unsynchronized replies of, 268
Beacon system, radar, 246-254
Beam shape, choice of, 600-604
Beamwidth of antenna, 20, 271
Bell Telephone Laboratories, 291, 565,
664

Bendix Aviation, 578, 580
Blackmer, L. L., 221
Blind speeds, choice of, 654
in MTI, 650
Blocking oscillator, 502
Boice, W. K., 560
Breit, G., 13

British Technical Mission, 15
Brush, high-altitude, for rotating ma¬
chines, 561
B-seope, 171
design of, 528-532

INDEX

739

B-scope, electrostatic, 528
magnetic, 528
Button, C. T., 578

Cable, coaxial, 397
Carlson, J. F., 65
Cathode follower, 494
Cathode-ray tube, 475-486
deflection coil of, 477
display projection of, 219
electrostatic deflection of, 476
electrostatic focusing of, 476
magnetic deflection of, 477
magnetic focusing of, 476
types of, 483

Cathode-ray tube screens, 479-483
cascade, 480
dark trace, 483
long-persistence, 480
supernormal buildup in, 482
Cathode-ray tube sweeps, delayed, 522
Cavities, resonant, 405-407
CH (see Home Chain)

Chaff, 82

Chain, Home (see Home Chain, British)

Channel, signal, 434

Chart projector, 215

Chokes, 397

Chu, L. J., 64

Circuit efficiency, of magnetron, 345
Cities, radar signals from, 101
Clamps, 503-508
switched, 505-508
Close control, 232-240
Clutter, 124-126
rain, 81

Clutter fluctuation, internal, 642-644
measured values of, 643
when radar is moving, 657
Clutter-noise, 651
CMH, 188

Coaxial-type mixer, 417
Coder, triple-pulse, 686
Coding (see Beacon, interrogation coding

of)

effectiveness of, 688
of pulses, 686

Coherence, ways of producing, between
echo signals and reference signal,
635-638

Coherent oscillator, 632
effect of detuning, 640
for MTI, 662-665
circuit design of, 663
Combined plan and height systems, 192
Complex targets, 73, 75-81
Component, r-f (see R-f components)
Compound targets, 73, 81
Computers, dead-reckoning, 215
Conical scan (see Scan, conical)
Connectors coaxial-line, 396
type N, 397

Contrast of PPI display (see PPI dis¬
plays, contrast of)

Control (see Speed; Voltage; etc.)
Controllers, 235
Corner reflector, 67

Cosecant-squared antenna (see Antenna,
cosecant-squared)

Counter, V. A., 80

Coupling, for coaxial line (see- Line,
coaxial, coupling for)
waveguide (see Waveguide, choke
coupling for)

Coverage, high, 50
low, 50

Coverage diagram, 54
Crest factor, 557
Cross section, of aircraft, 76
experimental, 78
corner reflector, 67
cylinder, 66
effective receiving, 20
flat sheet, 65

propeller modulation of, 76
radar, 21, 63
scattering, ,21
from sphere, 64
segment of sphere, 66
of ships, 80

CRT (see Cathode-ray tube)

Crystal, converter-type, specifications of,
414

for mixer, 412-414
noise temperature of, 413
C-scope, 173
Cut paraboloid, 272
C-w radar systems

(See also Radar system, c-w)

CXAM, 180

Cylindrical reflector, 276

740

RADAR SYSTEM ENGINEERING

Dark-trace screens, 483
Dark-trace tube, 220
Data stabilization, 311-312
Data transmission, 283
potentiometers for, 487
variable condensers for, 489
variable transformers for, 487
autosyns, 487
resolvers, 487
selsyns, 487
synchros, 487

Data transmitter, angle, 486—492
D-c restorer, 503

Deck-tilt error (see Error, deck-tilt)

Decoder, triple-pulse, 687

Delay line, characteristic impedance of,

671

folded mercury, 668
fused quartz, 669
laboratory type of, 633
liquid, 667-669

mercury, design constants for, 670
supersonic, 667-672
Delay-line attenuation, 670
Delay-line circuits, 634
Delay-line driving circuits, 672
Delay-line end cells, 669
Delay-line signal circuits, 672-675
Delay-line trigger circuits, 675-677
degenerative, 675
regenerative, 676
Delay tank, liquid, 669
Detection, aural, 134
Detector, balanced, for MTI, 666
second, 449
Dicke, R. H., 32
Diffraction cross section, 69
Diffraction phenomena at medium wave¬
length, 715
Diode, biased, 504
charging, 383
Diode limiters, 504
Display, double-dot, 174
one-dimensional, 164-167
three-dimensional, 174-175
two-dimensional, 167-174
pip-matching, 167
sector, 168

(See also Indicator)

Doppler effect, 125, 629
Doppler frequency, 128
Doppler system, bandwidth of, 135
pulsed, 630

pulse-modulated, 150-157
range-measuring, 139-143
simple, 132-139

Double-dot display ( see Display, double¬
dot)

Double-tuned circuit, 446
DuBridge, L. A., 16
Duct, 56-58
Dueppel, 82
Duplexing, 407-411
Dynamotors, 579-581
booster armature voltage regulation of,
580

dual-output, 579
triple-output, 579

Eagle ( see AN/APQ-7 scanner)

Eccles, W. H., 497
Eccles-Jordan circuit, 497
Echo, from rain, 81
fluctuations of, 83
reduction of, 84
second time around, 117
from storm, 81
Eclipse, 559, 574

Effective height, of ship target, 80
Eicor Inc., 579
Eighth-power region, 51
Electromagnetic energy storage, 356
Electronic efficiency, of magnetron, 345
Electronic switches, 503-510
Electrostatic deflection of beam of CRT
(see Cathode-ray tube, electrostatic
deflection of)

Electrostatic energy storage, 356
Electrostatic focusing of CRT (see
Cathode-ray tube, electrostatic fo¬
cusing of)

Elsey, Howard M., 561
Emslie, A. G., 640, 645
Error, deck-tilt, 309
in aircraft, 311
E-scope, 173

Evans Signal Laboratory, 17

INDEX

741

Fairbank, W. M., 80
Fan beam, 22, 274-277
Fast time constant circuit, 458
Feedback amplifiers (see Amplifiers, nega¬
tive feedback)

Feedback chains, 449
Feedback pairs, 449
Ferguson, A. J., 449
Fighter Control Center, 229-231
Fittings, type-N (see Connectors, type N)
555th Signal Air Warning Battalion, 229
Fletcher, R., 353
Flip-flop, 497
Flopover, 497, 498-499
Form factor, 557
Forward Director Posts, 229-240
Frequency modulation (see Modulation,
frequency)

F-m range measurement, multiple target,
147-149

F-m range-measuring system, 143-147
FTC (see Fast time constant circuit)

Gain, of antenna, 19
storage, 44

Gain-bandwidth product, single-tuned
stage, 446

double-tuned stage, 447
Gain control, instantaneous automatic,
459

GCA, 211

Gear boxes, aircraft, dual-outlet, 560
General Electric Company, 559, 565, 570,
571, 573, 574

General Radio Company, 664
Generator, aircraft, dual-purpose, 560
400-cps, permanent-magnet-field, 585
single stroke, 496
Glass, S. W., 561
Gordy, W. O., 80
Goudsmit, S. A., 65
GPI, 216

Gray, Marion C., 65
Ground control of approach (see GCA)
Ground-position indicator (see GPI)
Ground return, 92-96, 154
Guerlac, H. E., 13

Half-wave line (see Line, half-wave)
Hard-tube pulser (see Pulser)

Heat removal from r-f head (see R-f
head, heat removal from)

Height, effective, 52
Height-finding, 184-196
by elevation scanning, 189
by null readings, 184
by searchlighting, 187
by signal comparison, 185
Height-finding system, combined with
plan system, 192
Height indicator, V-beam, 547
Height indices, 518-524
Height markers, movable, 520
Hertz, Heinrich, 13

Holtzer-Cabot Electric Company, 574,
575, 576, 577, 578

Home Chain, British (CH), 175-180
organization of, 226-228
Homing, 196-203
on aircraft, 200
on surface target, 196
Hubbard, M. M., 560
Hudspeth, E. L., 80
Hulsmeyer, 13

IAGC (see Gain control, instantaneous
automatic)

Identification systems, (see IFF)

I-f amplifier (see Amplifier, i-f)

IFF, 251

Impedance, characteristic, 391
of delay lines, 671
internal, of pulser, 366
normalized, of waveguide, 401
Indication, true-bearing, 311
Indicator, classification of, 164
ground position (see GPI)
plan-position (see Plan-position indi¬
cator & PPI)
radar, 161-175
radial time base, 174
range-height (see Range-height indi¬
cator)

spot error, 175
(See also Display)

Indices, 163

742

RADAR SYSTEM ENGINEERING

Indices, of range and angle, 51 3-524
Inductance, nonlinear, as switch, 381
Inductance charging, 382
Integration, of radar information, 38-47
Interference absorber, 69
Interference lobes, 50
Intermediate frequency, choice of, 444
Intermediate-frequency amplifier (see
Amplifier, i-f)

Interrogator-responsor, 253
J

Jacobsen Manufacturing Company, 585
Jordan, F. W., 497
Josephson, V., 77
J-scope, 166

Judson Manufacturing Company, 585

Katzin, M., 80
Keep-alive electrode, 410
Keneipp, H. E., 560
Klystron, reflex, 414
Kock, W. E., 85
K-scope, 167

Lawson, J. L., 33
Lebenbaum, Paul, Jr., 561
Lee regulator, 574

Leland Electric Company, 570, 573, 574
Levoy, L. G., Jr., 560
LHTR, 208
Lighthouse tube, 207
Limiting of video output signal level, 452
Line, coaxial, 393-398
coupling for, 396
rotary joint for, 396
to waveguide, transition between,
403

half-wave, 392
long, effect of, 393
matched, 393
quarter-wave, 392
stub-supported, 395
Line-type pulser, (see Pulser)

Linford, L. B., 77
Loaded Q, 406

Lobe-switching, 203
Lobes, side, 272
Local oscillator, 8, 414—416
MTI, design of, 659-662
stability of, 638-640
Local-oscillator stabilities, typical, 661
Lockover, 497
L-seope, 167

Magnetic focusing of CRT (see Cathode-
ray tube, magnetic focusing of)
Magnetron, 7, 320-355
construction of, 321-325
electron orbits in, 330
frequency pulling of, 349
frequency stabilization of, 351
inductive tuning of, 347
input impedance of, 346
modes of operation for, 328
for MTI, stability of, 640
output coupling of, 329
performance chart for, 336
pulling figure of, 349
pulse-length limitations on, 346
pulse power of, 341
resonant system of, 325
rising sun, 330

space-charge distribution in, 335
strapped, 330
tunable, C-ring, 347
tuning of, 347
wavelength scaling of, 341
Magnetron cathode, back bombardment
of, 344

Magnetron efficiency, 345
Magnetron instabilities, 353
sparking, 353
mode-changing, 353
Marconi, G., 13

Markers (see Range, Timing, Angle,
Height markers)

Massachusetts Institute of Technology,
16

Mattress antennas, 274
Micro-B, 171
Micro-B display, 531
Microwave Committee, 15
Microwave propagation (see Propaga¬
tion of microwaves)

INDEX

743

Microwave, reason for use of, 10

attenuation of (see Attenuation of
microwaves)

Mixer, 8

coaxial-type, 417

crystal for (see Crystal, for mixer)
microwave, 416-418
Modulation, amplitude, 129, 139
frequency, 130
pulse, 130
from scanning, 136

Modulator, MTI requirements on, 641
(See also Pulser)

Morse, P. M., 65

Motor-alternator sets, aircraft, 561-563
speed regulators for, 571-578
starting current of, 561-563
Motor-alternator sets, speed control of,
574

Mount, antenna (see Antenna mount)
three-axis, 309
Mountain relief, 96-99
Moving-target indication (see MTI)
MTI, 626-679
basic principles of, 626-632
blind speeds in, 650
magnetron for, stability of, 640
on moving system, 655-658
noncoherent method of, 656
phase-shift unit for, 655
design of, 663

special test equipment for, 677-679
target visibility in, 649-653
trigger generator for, 634
MTI cancellation equipment, stability
requirements on, 641
MTI component design, 658-679
MTI component requirements, summary
of, 642

MTI components (see particular com¬
ponent)

MTI local oscillator, stability of, 638-640
MTI locking pulse, requirements on, 662
MTI operating tests, 677
MTI oscillator stability, testing, 677
MTI receiver characteristics (see Re¬
ceiver, MTI, characteristics of)

MTI requirements on modulator, 641
MTI system, practical, 632-635
MTI system constants, choice of, 638-655

MTI targets in clutter, visibility of, 651-
653

MTI transmitter, 658
Multivibrator, 497-500
cathode-coupled, 499
flip-flop, 498
single-stroke, 498
Myers, W. L., 283

National Defense Research Committee
(see NDRC)

Naval Research Laboratory, 14
Navigation, lightweight airborne radar
system for, 611-625
radar (see Radar navigation)

NDRC, 15
Division 17, 216
Neild, W. G., 569
Network, pulse-forming, 375
Newton regulator, 566-570
IX TAC, 229
Noise, 28—47

Noise figure, over-all receiver, 32, 441
Noise fluctuations, 35-40
Noise power, available, 30
Noise temperature, of crystal (see Crys¬
tal, noise temperature of)
Nonscanning antennas, 277-279
Nyquist, H., 30

Oboe system, 246-247
Odographs, 216
Olson, V. A., 655, 665
Optical superposition, of indicator scales,
218

Oscillator, local (see Local oscillator)
phase locking of, 632

Paraboloid antennas, 272-274
Peaking, series, 452
shunt, 451
Pedestal, 271

Performance chart, for magnetron (see
Magnetron, performance chart for)
Phantastron, 500
Phase locking of oscillators, 632
ir-mode, 326

744

RADAR SYSTEM ENGINEERING

Pillbox, 276
Pip-matching, 203
Plan-position indicator, 6, 167
(See also PPI)

Plotting board, 180°, 238
vertical, 235
X-Y, 240
Polyrod, 278

Polyrod radiators, array of, 303
Pound, R. V., 717, 724
Power, for mobile radar, 585

prime, supplies for radar, 555-587
for radar, in aircraft, 555-583
frequency of, 555
recommendations for, 582
at fixed locations, 583
for large systems, locally generated,
584

for shipborne systems, 586
Power frequencies, in aircraft, standard,
556

Power supply, 3-phase a-c radar, 559
for ultraportable equipment, 585
vibrator, 581
PPI, 167
delayed, 169
design of, 532-545
off-center, 168
open-center, 169
pre-time-base resolution for, 544
resolved-current, 538-545
resolved time base, 534-538
rotating-coil, 534
stretched, 170
three-tone, 553

using automatic transmitter triggering,
540

PPI displays, contrast of, 548-554
resolution of, 548-554
Pre-plumbing, 408
Pressurization, of r-f lines, 283, 420
PRF, choice of, 598
Prime movers, small, 586
Prime power supplies for radar (see
Power, prime, supplies for radar)
Projector, chart, 215
Propagation, free-space, 18

of microwaves, over reflecting surface,
47-53

(see also Microwave propagation)
PSWR (see Standing-wave ratio, power)

Pulse, phase-shifted, 697
sharp, generation of, 501-503
Pulse cable, 386

Pulse length, choice of, 596-598
Pulse modulation (see Modulation, pulse)
Pulse packet, 122

Pulse power (see Magnetron, pulse power
of)

Pujse-forming network (see Network,
pulse-forming)

Pulse-modulated doppler system, 150-157
Pulse-to-pulse cancellation, 631
Pulse recurrence frequency (see PRF)
Pulse transformers, 384-386
Pulser, 353-390
basic circuit, 356-360
driver circuit, 371
energy sources of, 387
hard-tube, 367-373

hard-tube and line-type, comparison
of, 360-363

line-type, 358, 374-383
a-c charging of, 383
recharging circuit of, 382
switches for, 377-381
overload protection of, 364
Pulser switch, 357
for line-type pulsers, 377-381
nonlinear inductance as, 381
Pulser switch tubes, high-vacuum, 368

Q, of cavity, 406

Quarter-wave line (see Line, quarter-
wave)

Quarter-wave plate, 84
R

Racons, 246
Radar, 419

comparison of, with eye, 1
c-w, 127-159

comparison with pulse radar, 123
ground, use of beacons with, 609
history of, 13
limitations of, 116-126
prime power supplies for (see Power,
prime, supplies for radar)
principle of, 3-6

INDEX

745

Radar, pulse, 3
range performance of, 8-10
word, 3

Radar beacon (see Beacon, radar)

Radar components, 6-8
Radar coverage, effects of surface reflec¬
tion on, 603

Radar cross section, 21, 63
Radar equation, 21-27
Radar horizon, 53
Radar indicator, 161-175
(See also Indicator)

Radar landmarks, 113
Radar navigation, 108-115
Radar performance figure, 590
Radar performance surveys, 592
Radar relay, 225, 680-735
AM vs. FM for, 717-719
antenna for, 713-719
antenna filter for, 720
frequencies used for, 716
100 Mc/sec, equipment, 721-723
300 Mc/sec, equipment, 719-721
uses of, 680

(See aho Relaying)

Radar relay analyzer, 682
Radar relay interference, combating, 685
Radar relay receiver design, 717
Radar relay r-f equipment, 682, 713-719
Radar relay scan converter, 682
Radar relay synchronizer, 681
Radar relay system, for airborne radar,
732-735

ground-to-ground, 726-732
maximum range of, 724
microwave, 723-726
simple, 681

Radar relay terminal equipment, 682
Radar relay transmitter design, 717
Radar scanning patterns (see Scanning
patterns, radar)

Radar system, 12

airborne, lightweight, for navigation,
611-625
c-w, 127-159

comparison with pulse radar, 123
summary of, 157-159
high-performance, for air surveillance
and control, 592-611
testing, 590
versatility of, 588

Radial time base indicator (see Indicator,
radial time base)

Radiation Laboratory, 16
Radio Corporation of America, 240
Radomes, 314
airborne, drag of, 315
electrical transmission of, 316
examples of, 317-319
sandwich construction of, 316
structural design of, 316
RAF Fighter Command, 226
Rain echo (see Echo, from rain, 81)
Ramandanoff, D., 561
Range equation, 595
Range-height indicator (RHI), 172, 545-
547

Range indices, 518-524
Range markers, movable, 518
Range scopes, 165-167
Range sweep, 162
Rapid photographic projection, 221
Ratio, standing-wave (see Standing-wave
ratio)

Rayleigh scattering, 63
Receiver, definition of, 435
general-purpose, 462-464
input circuits of, 442
lightweight airborne, 464-470
logarithmic, 553

MTI, adjustment of limit level in, 649
characteristics of, 646-649
comparison of types of, 648
limiting, 647, 665
lin-log, 647, 665
over-all noise figure of, 32, 441
radar, 433-474
typical, 460-474
Wideband, 470-474
Receiver bandwidth, 33
Receiver design, MTI, 665
Receiving system, typical, 435—441
Rectangular waveforms, generation of,
496-501

Reflection, diffuse, 89-92
specular, 89-92
Reflection coefficient, 49
Refraction, 53

Regulator (see Voltage, Speed, etc.)
Relaxation oscillator, free-running, 496
Relay radar (see Radar relay)

Relaying, of scanner data, 683

746

RADAR SYSTEM ENGINEERING

Relaying, of sine and cosine, general
methods of, 701-711
Repeater, electromechanical, 490-492
synchro-driven, 490
Resistance, back, of crystal, 413
spreading, of crystal, 413
Resolution of PPI display (see PPI dis¬
plays, resolution of)

Resolvers, 487
Resonance charging, 382
Resonant cavities (see Cavities, resonant)
Responder beacons, 246
R-f components, 391-432
R-f head, 419 432
examples of, 425-432
heat removal from, 421
test points in, 424
R-f switch, 295
R-f unit, 420
Rieke, F. F., 353
Rieke diagram, 339

Rising sun magnetron (see Magnetron,
rising sun)

Roberts, S., 662, 678
Robertson, L. M., 561
Robertson, R. M., 291, 295
Robinson, C. V., 298
Rotary joint, for coaxial line (see Line,
coaxial, rotary joint for)
for waveguide (see Waveguide rotary
joint)

Rotary spark gap, 381
R-scope, 165
Rubenstein, P. J., 64
Ryde, D., 62
Ryde, J. W., 62

Sawtooth generators, 510-514
Scale factor, 162
Scale markers, 163
Scale-of-two, 497, 499
Scan, complex, 281
circular, 281
conical, 188, 205, 281
helical, 281
horizon, 281
Palmer, 282
sector, 199, 281
simple, 280

Scan, spiral, 281
Scanner, 271

airborne, installation of, 312
electrical, 291-304
of long-range ground radar, 287
mechanical, 282-291
stabilization of (see Stabilization; Sta¬
bilizer)

surface-based, installation of, 313
weight of, 283

Scanning, conical (see Conical scan)
signal fluctuations due to, 644-646
Scanning loss, 43

Scanning modulation (see Modulation,
from scanning)

Scanning patterns, radar, 280-282
Scanning rate, 116-121
azimuth, choice of, 599
Schwarzschild antenna, 295-298
SCI height finder, 298-302
SCR-268, 203
SCR-270, 181
SCR-271, 181
SCR-521, 196
SCR-527, 186
SCR-540, 201
SCR-584, 207-210
close control with, 238
scanner, 284-286
SCR-588, 186
SCR-615, 188
SCIL627, 186
SCR^702, 202
SCR-717, 199
SCR-720, 201

Screens, cathode-ray tube (see Cathode-
ray tube screens)

Sea return, 92-96
Second-time-around echo, 117
Sector control, 230
Sector display (see Display, sector)
Sector scan (see Scan, sector)
Self-synchronous system, 438
Selsyns, 487

Sensitivity-time-control circuit, 460

Sequencing circuits, 710

Series gap switch, 377

Series peaking (see Peaking, series)

Servomechanisms, 491

Shunt peaking (see Peaking, shunt)

Side lobes, 272

INDEX

747

Signal, interference of, 73
minimum detectable, 28—47
minimum discernible, 34
Signal Corps Laboratories, 14
Signal fluctuations due to scanning, 644-
646

Signal loss caused by MTI, 651
Single-tuned circuit, 445
Skiatron, 220, 483
Skin depth, 406
Slug-tuned coil, 442
SM, 188

Spark gap, rotary, 381
Specular cross section, 69
Speed control, of motor-alternator sets,
574

motor-, electronic, 578
of motor, by voltage generator, 574
tuned-circuit, for motors, 577
Speed governor, carbon-pile, 578
Speed regulator, for aircraft motor-alter¬
nators, 571-578
motor-, Lee, 574
Spencer, R. C., 68
Stabilization, 304-312
airborne antenna, 305-308
frequency, of various components (see
various components)

8hipborne antenna, 308-312
Stabilizer, airborne, errors in, 308
line-of-sight, 306-308
roll, 306

shipborne, accuracy of, 311
stable-base, 306
Stagger damping, 449
Stagger-tuned circuits, 448
Standing waves, 391
Standing-wave ratio, power, 392
voltage, 392

Storage gain (see Gain, storage)

Storage tube, as delay device, 631
Storm echo (see Echo, from storm)
Straight line charging, 383
Strapped magnetron (see Magnetron,
strapped)

Stratton, J. A., 64
Straus, H. A., 295
Structures, radar signals from, 99
Stub support, broadband, 395
Subcarrier, phase-shifted, 695
Subcarrier method, 684

Superposition, optical, of indicator scales,
218

Superrefraction, 55

Switch (see ATR, R-f, TR, etc.)

pulser (see Pulser switch)

Switch tubes, high-vacuum, for pulsers,
368

Synchronization, 518-524
incremental angle, method of, 689-695
jittered-pulse system of, 693
phase-shift method of, 695-701
Synchronization methods for radar relay,
comparison of, 711-713
Synchronizer, radar relay, 681
Synchros, 487
Synchroscope, 164
System, back-of-the-dish, 419
radar (see Radar system)

Targets, complex, 73, 75-81
compound, 73, 81
extended surface, 85
Teleran, 240

Temperature, noise, of crystal (see Crys¬
tal, noise temperature of)

Test equipment for MTI, special, 677-
679

Thyratron, hydrogen, 379
Time base, 162
Time-sharing method, 684
Timing markers, discrete, 520-522
TR switch, 7, 407-411, 420
TR tube, 407
prepulsing of, 607

Tracking, automatic angle, 207-210
regenerative, of pulses, 707
Tracking circuit, locking in of, 710
Transducers, electromechanical, 667
Transformer, jog, 295

(see also type of transformer)
Transmission, c-w, of sine and cosine,
703-711

data (see Data transmission)
pulse, of sine and cosine, 704
Transmit-receive switch (see TR switch)
Transmit-receive unit, 420
Transmitter, data (see Data transmitter)
Transponders, 246
Trapping, 56-58

748

RADAR SYSTEM ENGINEERING

Trigatron, 379

Trigger generator for MTI, 634
Tube (see Cathode-ray tubes; Klystrons;
etc.)

Tuve, M. A., 13

Unloaded Q, 406

U.S. Tactical Air Commands, 229-240
V

Van Vleck, J. H., 59, 60
Variable Elevation Beam (VEB), 189
VEB (see Variable Elevation Beam)
V-beam (see Height indicator, V-beam)
V-beam radar, 193-196
Veinott, C. G., 560

Vibrator power supplies (see Power
supply)

Video, output limiting of (see Limiting of
video output signal level)

Video amplifier (see Amplifier, video)
Video mapping, 223
Video mixing, 45

Visibility, of MTI targets, in clutter,
651-653
subclutter, 653
measurement of, 679
of target, in clear, 649-651
in MTI, 649-653

Voltage regulation, booster armature, of
dynamotors, 580

Voltage regulator, for aircraft alternators,
563-566

carbon-pile, 566-570

Voltage regulator, carbon-pile, adjust¬
ment of, 567
shock-mounting of, 568
control of motor speed by, 574
finger-type, 570
mechanical, 566-571

VSWR (see Standing-wave ratio, voltage)
W

Wallman, H., 448, 449
Watson-Watt, Sir Robert, 14, 176
Wave shape of airborne alternators, 557
Waveform (see type of)

Waveguide, 398-405
attenuation in, 405
bends in, 402
choke coupling for, 401
to coaxial line, transition between, 403
cutoff frequency in, 400
modes in, 400

power-handling ability of, 404
of variable width, 291
wavelength in, 400
Waveguide rotary joint, 403
Wavelength, choice of, 604
in waveguide, 400

Waves, standing (see Standing waves)
Weinstock, Robert, 64
Williams, D., 77

Wincharger Corporation, 574, 576
Window, 81
Woodcock, W., 77

Yagi antenna (see Antenna, Yagi)

Yaw stabilization, 311

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